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UNIVERSITY OF ILLINOIS 
LIBRARY 


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A SERIES OF TEXTBOOKS FOR PERSONS ENGAGED IN THE ENGINEERING 
PROFESSIONS AND ‘TRADES OR FOR THOSE WHO _ DESIRE 
INFORMATION CONCERNING THEM. FULLY ILLUSTRATED 
AND CONTAINING NUMEROUS PRACTICAL 
EXAMPLES AND THEIR SOLUTIONS 


ANALYSIS OF STRESSES 
PROPORTIONING THE MATERIAL 
Gi romob CONSTRUCTION 2s 
DETAILS, BILLS, AND ESTIMATES 
STREETS AND HIGHWAYS 
PAVING 


SCRANTON : 
INTERNATIONAL TEXTBOOK COMPANY 


35 


iv PREFACE 


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In meeting these requirements, we have produced a set of 
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practical acquaintance with the use of the logarithmic table. 
To effect this result, derivations of rules and formulas are 
omitted, but thorough and complete instructions are given 
regarding how, when, and under what circumstances any 
particular rule, formula, or process should be applied; and 
whenever possible one or more examples, such as would be 
likely to arise in actual practice—together with their solu- 
tions—are given to illustrate and explain its application. 

In preparing these textbooks, it has been our constant 
endeavor to view the matter from the student’s standpoint, 
and to try and anticipate everything that would cause him 
trouble. The utmost pains have been taken to avoid. and 
correct any and all ambiguous expressions—both those due 
to faulty rhetoric and those due to insufficiency of statement 
or explanation. As the best way to make a statement, 
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almost without limit. The illustrations have in all cases 
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tions and sections or outline, partially shaded, or full-shaded 
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PREFACE V 


maximum of information in a minimum space, but this infor- 
mation is so ingeniously arranged and correlated, and the 
indexes are so full and complete, that it can at’ once be made 
available to the reader. The numerous examples and 
explanatory remarks, together with the absence of long 
demonstrations and abstruse mathematical calculations, are 
of great assistance in helping one to select the proper for- 
mula, method, or process and in teaching him how and 
non Lt shod be used. 

This volume treats on the subjects of bridge eae streets 
and highways, and paving. The subject of bridge design is 
introduced by two papers on Analysis of Stresses, which 
virtually form a continuation of the paper on Graphical 
Statics included in another volume. <A feature peculiar to 
the present treatment of bridge design is the fact that the 
graphical method of moments has been used throughout. 
Consequently the text can be readily understood by one who 
has no knowledge of algebra. The papers on Streets and 
Highways and Paving will prove valuable to the city engi- 
neer and to all interested in these important subjects. 

As mentioned above, this volume is printed from the 
plates used in printing the Reference Libraries of the Inter- 
national Correspondence Schools. On account of the omis- 
sion of certain papers, the material contained in which is 
given in better form elsewhere, there are several breaks in 
the continuity of the page numbers, formula numbers, article 
numbers, etc. This, however, does not impair the value of 
the volume, as the index has been reprinted and made to 
conform to the present arrangement. 


INTERNATIONAL TEXTBOOK COMPANY. 





CONTENTS 


ANALYSIS OF STRESSES Page 
The Pruss-- - - - - - - - = SOS0 
Loads “= 3 : . - - - - - 690 
Maximum Live-Load Chord Stresses - - - 694 
Maximum Live-Load Web Stresses” - - - 699 
Dead Load - - - - - - ” - (04 
Counter Stresses - - - - - - + fang 
Wind Stresses é - - - - - « %11 
Stresses in Latticed Portal - - - Sire {il ts: 
Floorbeam Stresses - - - - - ~ ae eo 
Stress Sheets : - - - - - - (32 
Method by the Moment and Shear Diagrams - 733 
Short Method for Web Stresses .- - - - 437 
The Howe Truss - - - - - . oj eel 
The Warren Girder’~ - - - - - - %44 
Trusses with Inclined Chords - - - - %49 
The Whipple Truss — - : - : - - F793 
The Baltimore Truss - - - - - ee i he: 
The Petit Truss - - - - - - - %86 
Stresses in Braced Portal - - - - al Ut SID 
Floorbeams With Sidewalk Cantilevers - sty oo 
Concentrated Wheel Loads - - - - = OL 

PROPORTIONING THE MATERIAL 
Materials Used for Bridge Superstructures - are BDF 
The Use of Wrought Iron - - - - - 812 
Unit Stresses Allowed for Tension Members - 814 


Proportioning the Material for Tension Members 817 
Compression Members: Radii of Gyration# - 819 
Vil 


” 


vill CONTENTS 


PROPORTIONING THE MATERIAL—Continued Page 
Weight of Wrought Iron” - : : : ae eras 
Proportioning the Material for Compression Mem- 

bers - - - . - - a Pao 
Effect of Wind Stress on Chords and End Posts 850 
Proportioning the Material for Floorbeams - 859 
Cheshioor - . - - - - ©) 1865 
Completing the Stress Sheet “ x - - 866 
The Use of Steel - - - - - . - 868 
The Fatigue of Metals - - - : - - | (872 


Items from Thacher’s and Lewis’s Specifications 875 
Weight and Specific Gravity of Wrought Iron 


and Steel - - - - - - - - 878 
Eccentricity; Position of Pins; Bending Stresses 

Due to Weight of Member - - : - 880 

DETAILS OF CONSTRUCTION 

General Requirements - - - > - - 895 
Specifications - - - . - - oe eh Mi 
Camber - - - - . - - - 903 
Exact Length of Diagonal Members - - - 905 
Positions of Pins in Chords and End Posts - - 908 
General Dimensions of Upper Chord and End 

Post - - . - - - - - 2 Poot) 
Clearance - - - - - - - =. OLE 
Size of Pins - - - - - - - a es a 
Proportioning Pin Plates” - - - - - 914 
Moments on Pins - - - - - - - “925 
Constructive Details of the End Post - - - 94] 
Details of the Upper Chord - - - - - 948. 
Constructive Details of the Intermediate Post - 951 
Constructive Details of the Portal Bracing - - 958 
Constructive Details of the Lateral Struts and 

Knee Braces’ - - - . - - ry aon 
Constructive Details of the Floorbeam - - 966 
Eyebar Heads_~ - - - - - - = 2D 


Constructive Details of the Lower Chord Mem- 
bers - - - - - - - - sp ia 


DETAILS OF CoNSTRUCTION—Continued 
Constructive Details of the Tension Web 


bers - - 


Constructive Details of the Lateral Rods 
Constructive Details of the Beam Hanger 


DETAILS, BILLS, AND ESTIMATES 
Shoes, Rollers, and Bedplates 


CONTENTS 


Chord Pins, Pin Nuts, Cotter Pins, and 


Washers. - 
Shop Lists. - 
Iron Order - 
Lumber Bill- 
Shipping Bills 


The Erection Diagram 
The Approximate, or Preliminary, Estimates 
The Close Estimate 


Metal Joists and Stringers - 


Positions and Connections of Floorbeams 
Name Plates and Railings 
Paint and Painting 


Imperfect Design and Inconsistent Requirements 


STREETS AND HIGHWAYS 


Country Roads and Highways 


Construction of Roads - 


Maintenance of tlighways 
City Streets and Avenues 


PAVING 


Resistance to Traction 
Traction Power of Horses 


General Considerations Relating to Pavements - 
Paving Materials - 
Stone Pavements - 
Wood Pavements - 


Asphaltum and Coal-Tar Pavements 
Brick Pavements -~ 


Curbing and Footways 


—~ 


1X 
Page 


986 
992 
998 


1005 


1017 
1027 
1054 
1044 
1048 
1053 
1054 
1060 
1062 
1066 
1071 
1075 
1082 


995 
1031 
1037 
1040 


1101 
1108 
Litt 
1129 
1141 
1147 
1154 
1170 
1172 





PSN AIVGIS OF SERESSES. 


THE TRUSS. 


1267. A truss is a simple framed structure composed 
of straight members so connected as to act as one rigid 
body. While the truss as a whole resists the effect of the 
external forces acting upon it in much the same manner as 
shear and bending moment are resisted by a solid beam, 
each individual member of the truss is subjected only to 
direct tensile or compressive stress in the direction of its 
length. In order that this may be the case, the external 
forces must be applied at the joints of the truss, through 
which they act upon the structure as a whole. 


1268. The simplest possible truss is a triangle, and 
any truss is merely an assemblage of connected triangles. 
_As the triangle is a rigid figure whose form can not change 
so long as the length of each of its sides remains the same, 
it is the primary and essential element of the truss. A short 
definition of a truss was given in Art. 1120. 


1269. The external forces are the loads, including 
the weight of the structure itself, and the supporting forces, 
or reactions, all of which tend to distort the structure or 
change its form. 


1270. In bridge engineering any framed structure so 
designed that the reactions from the superimposed static 
loads are vertical is considered to be a truss. This dis- 
tinguishes the truss bridge from the arch and the 
suspension bridge, in which the reactions are not vertical. 


1271. A symmetrical truss is a truss having both 
ends alike; if it could be folded at the center upon itself in 


For notice of copyright, see page immediately following the title page. 


686 ANALYSIS OF STRESSES. 


such manner that the two ends would come together, all 
corresponding members in the two halves of the truss 
would coincide. Nearly all trusses are symmetrical. 


1272. A simple truss is a truss szmply supported; 
that is, a truss whose ezds simply rest on the points of sup- 
port without being rigidly fixed to them. It is similar toa 
simple beam, and is distinguished from a continuous 
truss or a cantilever truss by the same characteristics 
that distinguish a simple beam from a continuous or a 
cantilever beam. (See Arts. 1222 to 1226.) 


1273. The theoretical span of a simple truss is the 
distance between the centers of its supports. The truss is 
divided into a certain number of parts or sections, usually 
of equal length, called panels. The panel lengths are 
the horizontal distances between the joints of the loaded 
chord. A truss that is divided into five panels is called a 
five-panel truss; a truss divided into six panels is called 
a Six-panel truss, etc. Likewise, a bridge whose trusses 
are each divided into six panels is called a six-panel 
bridge. | 

The stresses in simple, symmetrical trusses only will be 
analyzed in the following pages. 


THE MEMBERS OF A TRUSS. 


1274. The names applied to the various members of a 
simple truss are given in Mechanical Drawing, Art. 54, in 
connection with and preceding Plate, Highway Bridge: 
Details I, to which reference may be made for the name of 
any member. 

When mentioned without reference to their positions in 
the truss, those members which resist compressive stresses 
are called struts, or compression members, and those 
which resist tensile stresses are called ties, or tension 
members. Each individual member, however, is usually 
designated with reference to its position in the structure. 





ANALYSIS OF STRESSES. 687 


When the diagonal members of a truss are compression 
members, they are called braces; the counters are called 
counterbraces. Inclined end posts are often called 
batter braces. 


1275. A compression member can resist a certain 
amount of tension also; but a member designed to resist 
tension only is not usually capable of resisting compression. 
When it is desired that a tension member shall resist a small 
amount of compression also, the form of the member must 
usually be changed. 


1276. When the loads upon a simple truss are down- 
wards, as is usually the case, the upper chord is always in 
compression, and the lower chord always in tension, In the 
web system the struts and ties alternate. 


1277. The extremities of each member are connected 
as nearly as possible on a line passing through the center of 
gravity of its section; the stress in a member is considered 
to act in a direct line between the centers of its connections, 
and, therefore, the member itself must be straight. For 
all purposes relating to the investigation of the stresses in 
the members of a truss, each member may be represented 
simply by a straight line indicating the line of action of its 
stress. 


CLASSIFICATION OF BRIDGES. 


1278. 4ridges are classified according to the positions 
wn which their roadways are supported. 

Deck bridges are those that support their roadways or 
loads at or near the levelof the upper chord. In this class 
of bridge all portions of the structure are entirely below 
the roadway, and are not visible from above it. Deck 
bridges require considerable space below the roadway, and, 
therefore, the locations to which they are adapted are not 
very common. 


1279. Through bridges are those that support their 
roadways at or near the level of the lower chords; the loads 


688 ANALYSIS OF STRESSES. 


pass between the trusses, or through the bridge. Bridges of 
this class are very common. If, in addition to the roadway, 
they also carry separate footways, the latter are usually 
supported outside of the trusses. 


1. High-truss bridges are those bridges of this class 
in which the trusses are of sufficient height to require a sys- 
tem of overhead lateral bracing to be placed between the 
upper chords above the roadway. ‘This class of trusses is 
not well adapted to spans of less than 80 feet. 


2. Low-truss bridges are those in which the trusses 
are not of sufficient height to require a system of lateral 
bracing above the roadway ;. such trusses are also designated 
as pony trusses. This class of bridges is adapted to short 
spans only. 


1280. Half-deck bridges support their roadways at 
some required elevation de¢ween the upper and lower chords. 
‘They are not very common. 


1281. A general classification of truss bridges may also 
be made according to the manner in which the members are 
connected. 

Pin-connected bridges are those in which the several 
members of the truss that meet at each joint are connected, 
and transmit their stresses, by means of an accurately 
turned pin, somewhat resembling a large bolt, which is 
made to fit very closely into holes drilled through the ends 
of the members. This affords a simple and convenient 
means for connecting the members. As the connection acts, 
to some extent, like a large hinge, it allows each member 
to readily adjust itself in the line of its stress without 
developing bending stresses. In this type of truss, each 
member can be practically finished at the shop; and, in 
erecting the bridge at its site, the members are assembled 
and connected, and the structure completed in the shortest 
possible time and with the minimum amount of field labor. 
Owing largely to this fact, the pin-connected type of bridge 
has become very popular in America. 





ANALYSIS OF STRESSES. 689 


1282. Riveted girders is the name commonly applied 
to those bridges in which all connections are riveted; certain 
forms of such bridges are also designated as riveted trusses 
and latticed girders. This type of structure is, by some 
engineers, very highly commended for spans of about 150 
feet or less. For spans lessthan 100 feet, they undoubtedly 
possess some advantages over pin-connected bridges; but 
whether this be true for spans greater than 100 feet may be 
seriously questioned. It must, however, be conceded that 
the tendency of the best modern practice is towards such 
details as will connect the truss as a rigid whole. 


1283. Under the preceding head may also be classified 
the type of structures known as plate girders, which are, 
within the limits of their availability, the best metal bridges 
known.. But they are not trusses—rather a distinct class of 
girders. 


1284. Trusses may be further classified according tothe 
form of their design; that is, according to the arrangement 
of the members and the form of the truss asa whole. But 
such classification will not be further noticed at present. 
Several forms of trusses will be discussed in their proper 
place. 

The truss represented in Mechanical Drawing Plate, Title: 
Highway Bridge: General Drawing, is of a design which, for 
bridges of ordinary span, is very common and popular in 
America. It is a pin-connected, high-truss, through bridge, 
of the type commonly known as the Pratt truss; though 
it is also known as a single-intersection and single- 
quadrangular truss. Substantially this form of truss 
was patented in 1844 by Thomas W. and Caleb Pratt as a 
combination wood and iron bridge. It is the favorite style 
of truss now used for moderate spans, and is usually con- 
structed entirely of metal. As a metal structure it pos- 
sesses advantages over all other forms of trusses. As this 
truss affords a simple and very practical example, all im- 
portant phases of its design will be noticed in their proper 
connection. 


690 ANALYSIS OF STRESSES. 


LOADS. 


1285. Under ordinary conditions, a bridge must be de- 
signed to carry or resist three different characters of external 
forces or loads. 


I. The live load on a bridge is the load it must carry, 
exclusive of its own weight. Usually the live load moves 
over the bridge, and for thisreason it isalso called moving 
load. For highway bridges, the live load is assumed at a 
specified amount per square foot of roadway or a specified 
amount per lineal foot of structure. -This load is assumed 
to be uniformly distributed over the roadway, and is known 
as a uniform load. For bridges so located as to be sub- 
jected to the passage of heavy loads concentrated upon 
wheels, the uniform load is augmented by certain assump- 
tions of concentrated loads or wheel loads. For rail- 
road bridges the live load usually consists of a system of 
concentrated wheel loads, or of certain assumed uniform 
loads that will give an approximately equivalent effect. 

The amount of live load which a bridge is designed to 
carry is often called its capacity. 


Il. The dead load on a structure is the weight of 
the structure itself. The terms bridge weight, fixed 
load, and static load are also sometimes used in the same 
sense. The latter term is not so strictly applicable, as the 
live load also is treated as a static load. The dead load 
is generally considered as a uniform load; it is assumed at a 
uniform amount per lineal foot of structure. 


III. The wind load is the load due to the force of the 
wind against the side of the structure. It must be resisted 
by the lateral systems. The wind load is usually assumed 
sufficiently large to also include and provide for the effect 
of such lateral vibrations in the trusses as are likely to be 
caused by the passage of heavy or rapidly moving loads 
across the structure. When specified, the amount of wind 
load per lineal foot assumed for each (loaded and unloaded) 
chord is usually stated. 


“ANALYSIS OF STRESSES. - 691 


PANEL CONCENTRATIONS. 


1286. The amount of load which is transferred to 
and supported at each joint of the loaded chord is called a 
panel concentration. In the case of a uniform load, 
each panel concentration is equal to one-half of the load 
supported by one truss upon the two panels adjacent to the 
_ joint, and is called a panel load. 


1287. The live load per square foot multiplied by the 
clear width of roadway gives the live load per lineal foot. 
This is the roadway load. When the bridge carries side- 
walks, the sidewalk load per lineal foot, found by multiplying 
the sidewalk load per square foot by the combined clear 
width of both sidewalks, must be added to the roadway load. 


1288. One-half the live or dead load per lineal foot 
multiplied by the panel length gives the panel live load or 
panel dead load, as the case may be. That is, this gives the 
amount of live or dead load to be carried by each joint of 
the loaded chord in one truss, it is the panel load to be 
used in finding the stresses. 


1289. The wind load per lineal foot, assumed or com- 
puted, for either chord, multiplied by the panel length, gives 
the panel wind load for that chord. 


EXAMPLE.—A bridge 99 feet long is designed to sustain 100 pounds 
per square foot upon a roadway 16 feet wide, clear width. The trusses 
are divided into 6 panels. What is the live load per lineal foot, and 
the panel live load ? 


SoLuTIon.—The live load per lineal foot equals 100 « 16 = 1,600 Ib. 
The panel length equals 0 = 16.5 ft- ‘Therefore, the panel- live load 


6 
1,600 « 16.5 
2 


equals — = 13,200 Ib. 


EXAMPLES FOR PRACTICE. 

1. In the preceding example, if the wind load assumed for the 
lower chord is 300 pounds per lineal foot, and that assumed for the 
upper chord is 150 pounds per lineal foot, what is the panel wind load 
(a\ for the lower chord, and (4) for the upper chord ? 

(a) 4,950 Ib. 
Ans. 4 () 2,475 Ib. 


692 ANALYSIS OF STRESSES. 


2. An eight-panel bridge of 120 feet span carries a roadway 18 feet 
wide in the clear. The live load assumed for the trusses is 96 pounds 
per square foot of roadway. What is (a) the live load per lineal foot, 
and (6) the panel live load ? Ae 1 (Dak, boon los 

" € (6) 12,960 Ib. 

3. If for the bridge of the preceding example the wind load per 
lineal foot is assumed at 3800 pounds for the lower chord and 150 
pounds for the upper chord, what is the panel wind load (a) for the 
lower chord, and (4) for the upper chord ? Are (a) 4,500 Ib. 

* € (6) 2,250 Ib. 

4. Suppose for the same bridge the dead load were assumed to be 
760 pounds per lineal foot, what would the panel dead load be ? 

Ans. 5,700 Ib. 


STRESSES FROM VARYING LOAD. 


1290. In taking up this subject, a comparison of the 
stresses in the members of a simple truss under different 
conditions of load will first be made. 

In solving Question 568, the student drew the stress 
diagram, and determined the stresses for a truss of three 


b ¢ cee 








a 4} aay: pe 
ze 
ty 
A 
R, 
7 e 
Scale 122400 lbs. 
FIG. 267. 


panels, carrying two loads, W, and W,, equal to 4,200 pounds 
each. In Fig. 267 is represented the same truss loaded 
with W, only, the load JV, having been removed: 

For this condition of load, the left reaction Rk, = 4,200 x 
12 24 


1 1,400 pounds and &, = 4,200 x 36 = 2,800 pounds. 


ANALYSIS OF STRESSES. 693 


At the left of the trussis shown the stress diagram. The 
line a6 f ais the load line, or polygon, of the external 
horeeseia, Wand) A, laid of in order.’ For joint 7, the 
polygon a 6 ¢ a is completed; and the polygon a cda is 
drawn for joint 2. For joint 8, arrow-heads are marked on 
dcandc 0 in reversed positions and directions; but it is 
found impossible to return the pencil from @ to the starting 
point d by a line parallel to G 4, the only remaining mem- 
ber which connects at joint 3. Therefore, another member 
must be introduced into the truss, connecting at joint 3, in 
such manner that the polygon for this joint can be com- 
pleted by lines drawn parallel to the additional member 
and to Gib. Ae member 1G, connécting joints 3 and 4, 
as indicated by a dotted line, is found to fulfil this con- 
dition; and the polygondc 6 g d may be completed for joint 
8 by drawing the lines 0 gand gd parallel to b Gand G D 
respectively. For joint 4, the polygon is ad gea, and 
egbfeisthe polygon for joint 8. A check upon the cor- 
rectness of the work is obtained in this polygon, as 6 / 
represents the load BF, or W,, 

The polygon for joint 6 is a e fa, in which fa represents 
R,. The two arrow-heads on each line indicate in each 
case the sense of the force with reference to the joint for 
which each arrow-head was used. 

Measuring with the scale used in laying off the load 
line, and designating compression by the + and tension by 
the — sign, the lines of the stress diagram are found to rep- 
resent the following values: 


ac=+ 2,780 b c= — 2,400 
c d= — 1,400 b g = — 4,800 
dg=+2,780 Jf e= — 4,800 
£e= — 4,200 ad= -+ 2,400 
ea=-+ 5,560 


1291. A comparison of the above stresses with those 
obtained for the corresponding members (notation slightly 
changed) in the solution of Question 568, is instructive. 

The very prominent and noticeable difference between 


694 ' ANALYSIS OF STRESSES. : 


the two cases is that, while, with the two equal loads upon 
the truss, no diagonal member is required in the center 
panel, when one of the loads is removed, the diagonal mem- 
ber is required. It is evident that if the truss were loaded 
with W, only, instead of W,, the diagonal 3-4 would be in 
tension, instead of in compression. As in most types of 
structures, such diagonals are usually designed to resist ten- 
sion only or compression only, it would be the general prac- 
tice to put two diagonals in this panel, one connecting 
joints 3 and 4, and one connecting joints 2 and 35. 

When a truss ts partly loaded in a certain manner, mem- 
bers are required which do not act when the truss ts fully 
loaded. 

But it is also noticed that, when the truss carried’ two 
loads, the stresses in the chords and end posts were greater 
than when it carried one load. ‘These facts illustrate the 
following general principles: 

The maximum stresses in the chords occur when the whole 
truss 1s loaded; but the maximum stresses in the other 
members occur when the truss 1s only partly loaded. What 
the condition of loading should be in the latter. case will be 
explained further on. 


THE MAXIMUM LIVE CHORD STRESSES. 


1292. A live load will now be assumed for the bridge 
represented in Mechanical Drawing Plate, Title: Highway 
Bridge: General Drawing, and the maximum stress in each 
member due to the assumed load will be obtained by draw- 
ing the necessary stress diagrams. As has been stated, the 
theoretical length of the span ofa bridge is the length 
from center to center of end pins, 1.-e., the pins in the shoe 
joints. Inthe present case, the distance between the cen- 
ters of the pins in joints a and a’ is 90 feet; it is divided 
into five equai panels of 18 feet each. The clear width of 
roadway, that is, the clear width between trusses, is 18 feet, 
and the height of the trusses, between centers of chord 
pins, is 18 feet. 

The general dimensions of a bridge, such as have just 


ANALYSIS OF STRESSES. 695 


been given, together with the loads and such other infor- 
mation as may be necessary to make a proper design of the 
same, are called the data for the bridge. 

The live load will be assumed to be 100 pounds per square 
foot. s Lnelive load per lineal foot is, therefore; LOO x 18 = 
1,800 pounds. (Art. 1287.) This load is assumed to be 
applied upon any or all portions of the floor, in such man- 
“ner as to cause the maximum stresses in the several mem- 
bers. By means of stringers the load upon the floor is 
transferred to the floor beams or cross girders, which are 
placed across and beneath the roadway at the lower chord 
joints 0, c, c’, and J’. The stringers and floor beams act 
independently of the truss proper, serving simply to con- 
centrate the floor load upon the lower chord joints. 

The amount of lve load supported by one floor beam 
equals the load per lineal foot multiplied by the panel 
FeroenOres), 500% 18-52, 400) pounds... One-half ‘this 
amount, or 16,200 pounds, constitutes the panel load for 
one truss. (Art. 1288.) When the general dimensions of 
the truss are given, having ascertained the amount of live 
load that should be assumed for it, and the points at which 
the panel loads are concentrated, we have all the data re- 
quired for determining the stresses due to live load. 

The stresses are found for one truss, those for the other 
truss being usually identical. If the trusses have not the 
same form, the stresses must be found for each separately. 

As previously stated, the greatest stresses are developed 
in the chords and end posts when the bridge is fully loaded. 
This condition of load will first be considered, the values 
of the reactions will be computed, and the stress diagram 
drawn to find the live load stresses in the chords and end 
posts. 


1293. That portion of the load upon each end panel 
which ts carried directly by the abutment does not affect the 
truss. 

With the bridge fully loaded as above, one-half of each 
-end panel load is carried by the corresponding abutment. 


696 ANALYSIS OF STRESSES. 


Therefore, ina truss having panels of equal length, fully 
loaded with a uniform load, the reactions affecting the truss 
have the following values: 


W (x — 1) 
2 


isi = se == ’ (89.) 


in which W represents the panel load, and z the number of 
panels. 









Scale 1-24000 Lbs. 


6 11 
FIG. 268. 
In the present case, therefore, A, = A= o= xX 16,200 = 


32,400 pounds. In Fig. 268 is represented a diagram of the 


ANALYSIS OF STRESSES. 697 


truss, together with a stress diagram for this condition of 
ioagdee Here i") etc.) represent ‘the, pariel loads, -or 
16,200 pounds each. 

Bow’s system of notation is used, but numerals are used 
, instead of letters, because it is desired to use letters to 
designate the joints. .Each member of the truss will be 
designated by the letters of the two joints at which it con- 
nects, as members a 4 (not member 1-7); but the stress for 
a will be designated as 1-7, referring to the line of the 
stress diagram. 

In drawing the stress diagram, it will be found that the 
condition of equilibrium can be fulfilled for all joints with- 
out requiring stress in any of the members represented by 
dotted lines. When the truss is fully loaded with a uniform 
oceabereuisenostress anathe members. Cc). C.c’, Ce’, 
and 'G' ¢. 

The load line 2-6 is laid off by taking the external forces 
in order, beginning with X#, and passing to the right across 
the truss, or, in other words, beginning with #,, and taking 
the forces in order, passing to the left around the truss, as 
though they were forces acting upon a single point. By 
acting through the medium of the truss the forces bear the 
same general relation fo each other as though acting upon 
the same point. On the load line, therefore, 1-2 is laid off 
upwards equal to &, = 82,400 pounds, then 2-3, 3-4, 4-5, and 
5-6, each equal to a panel load = 16,200 pounds, are laid off 
downwards, and finally 6-7, equal to X, = 32,400 pounds, is 
laid off upwards to the starting point. 

Commencing with #,, the polygon /-2-7-1 is completed 
for joint a, 7-2-5-8-7 for joint 6, and 1-7-8-9-1 for joint B. 
For joint c, retrace 9-8 and 8-3 (that is, mark reversed 
arrow-heads, and consider them drawn from 9 to 8 and from 
8 to 8 respectively. [See Art. 1148]); pass downward on 
the load line the amount 3-4, equal to IV; a line returning 
from 4 to the starting point 9 will represent the equilibrant 
of the forces 9-8, 8-3, and 3-4, that is, will represent the. 
remaining force which acts upon this joint. As the closing 
line 4-9 is a horizontal line, it 1s evident that it must 


> 


698 ANALYSIS OF STRESSES. 


represent the stress in a horizontal member, which must 
necessarily be the member ¢ c’, this being the only remaining 
horizontal member which connects at this joint. As 4-9, or 
the stress in cc’, fulfils the condition of equilibrium for this 
joint, the members Cc and C’c, represented by dotted 
lines, do not act with this condition of load. For joint c’, 
retrace 9-4 (that is, mark a reversed arrow-head, and con- 
sider it as drawn from 9 to 4); pass downwards on the 
load line the amount 4-5; it will be found that from 4 the 
pencil can be returned to the starting point 9 by the lines 
5-10 and 10-9, drawn parallel toc’ d' and c' J’, respectively. 
The conditions at this joint are the same as at joint ¢, 
except that the positions of the forces are reversed; the 
condition of equilibrium is fulfilled without requiring the 
members Cc'-and C’c''to act: Ihe polygons for joints 
L' b' and a’ are substantially the same as for joints & 6 and 
a, respectively, and will be readily understood without 
special explanation. From an inspection of the stress 
diagram it is evident that the members represented by the 
dotted lines would not be required to act when the truss is 
fully loaded with a uniform load. For, in drawing the force 
polygon for joint c, the point 4 falls at the point 1, showing 
that the entire vertical force of the left reaction #,, repre- 
sented by 1-2, is entirely absorbed by the loads IW, and W,, 
represented by 2-3 and 3-4. Likewise, the right reaction 
R, (= 6-1) is absorbed by W, (= 4-5), and W,(= 6-6), and 
between joints ¢ and c’ no vertical forces are acting. To 
express this in the usual language, there zs no shear in the 
panelcc'. The effect is the same as though W, and W, 
were supported by &,, and W, and W, were supported by X&,,. 
By measuring the lines of the stress diagram, and using 
the conventional signs for tension and compression, the 
following values of the stresses are obtained : 
Stress ina B = 1-7 =-+ 45,820 lb. 
Stress in'a’ B' = 1-11 = + 45,820 lb. 
stressin £4’ = 1-9 =-+ 48,600'lb, 
Stressini gb “= 2-7 = —32.4004D: 
Stress in dc = 8-8 = — 32,400 lb, 


ANALYSIS OF STRESSES. 699 


Stress incc’ = 4-9 = — 48,600 lb. 
Stress inc’ 6’ = 6-10 = — 32,400 Ib. 
Stress in &'a’ = 6-11 = — 382,400 Ib. 
Stressin Be = 8-9 = — 22,910 lb. 
Stress in B’c’ = 9-10 = — 22,910 lb. 
Diteesitiwae a veo) = 62 00Nb, 
Stress in Bd’ = 10-11 = — 16,200 lb. 


NoTe.—The above stresses are given to the nearest ten pounds. In 
order that the student may better judge of the accuracy of his work, 
the stresses will be so given in what follows. But in actual practice it 
is never necessary to obtain the stress in any member of a bridge or 
similar structure closer than to the nearest hundred pounds. 

It is noticed that the line 7-9 represents compression, while 
tie line 4-9 represents tensiom. © As these lines coincide, .the 
student must be careful to distinguish the proper character 
of stress foreach. The above stresses are the maximum 
live load stresses in the chords and end posts. As the office 
of the hip verticals £ 6 and 4’ v' is simply to suspend the 
panel loads at 6 and 0' from the joints 4 and 4’, respect- 
ively, it is evident that the greatest stress which can come 
upon either of these members is the panel load which it 
supports. Therefore, the above stresses for Bdand B' 0’ 
are also Maximum. 


THE MAXIMUM LIVE LOAD WEB STRESSES. 


1294. Thestressesas found above for the web members 
He and J’ c’, however, are not. maximum. The maximum 
stresses in these and the remaining web members will occur 
under different conditions of load. 

Since the two ends of the truss are alike and are acted 
upon in the same manner by external forces of the respect- 
ive magnitudes, the stresses in the two halves of the truss 
are identical, and it is necessary to construct the stress dla- 
gram for those members only whose stresses are caused by 
one reaction. 

in the present case, the upper half of the stress diagram 
is the only portion necessary to be drawn. Although the 
complete stress diagram is sometimes drawn for the purpose 

I. Il,.—6 


700 ANALYSIS OF STRESSES. 


of checking the work, it is customary to obtain only those 
stresses due to the left reaction. This practice will gener- 
ally be followed hereafter in obtaining the live load stresses; 
the stress diagram will usually be drawn for those stresses 
only which are produced by the left reaction and the cor- 
responding loads. When stress in any member is men- 
tioned, it will be understood to mean stress caused by the 
left reaction; the stress in the corresponding member in the 
opposite half of the truss, caused by the right reaction, will 
be of the same character and magnitude. The maximum 
stresses in the web members will now be found. 


1295. ln a Pratt truss, the maximum stress will occur 
in the diagonal web member in any panel when all joints at 
the right of the panel are fully loaded and the joints at the 
left of it are not loaded. This condition will also give the 
maximum stress (of opposite character) in the vertical member 
which meets the diagonal in the unloaded chord. 

This rule, of course, does not apply to the hip vertical, 
whose maximum live load stress zs always equal to one panel 
load. 

The maximum stress in the tie 4c will occur when the 
joints c, c’, and 0’ are loaded, and joint @ is not loaded. In 


54+ 36418 6 


this condition FR, = 16,200 x 90 LO oO aes nia 


19,440 pounds. 

In Fig. 269 is represented a diagram of the truss and that 
portion of the stress diagram necessary to determine the 
stress in Ac. Those diagonal web members which transfer 
their load to the right reaction are omitted from the diagram 
of the truss. The load line 1-2 is laid off to scale equal to 
Rk, and the polygon J1-2-7-1 is completed for joint a. For 
joint J, the line 7-2 is first retraced; as there is no load at J, 
or, in other words, as the load at 0 is zero, the portion of 
the load line 2-3, which represents this load, has no magni- 
tude. In the stress diagram, therefore, the points 3 and 
2 will coincide; the line 3-8 will coincide with the line 7-2: 


) 


and as the terminus of the last line of the polygon must 


ANALYSIS OF STRESSES. 701 


close upon the starting point, it is evident that no stress can 
Bemobeainedsforsthe inember) bo ~For joint 6) retrace 
1-7 (that is, mark a reversed arrow-head, and consider it as 
drawn from i to 7), and, as there is no stress in & @, the 
pencil is returned to the starting point 7 by lines 7-9 and 
9-1, drawn parallel, respectively, to B c and C B. (These 
lines, of course, are actually drawn from 7 and J, respect- 





a 


FIG. 269. 


ively, their intersection locating the point 9.) In other 
words, 1-7-8-9-1is the polygon for joint 4. The line 8-9 repre- 
Ssehits tue Maximum stress in bc. As this feiure-is not a 
complete stress diagram, the arrow-heads marked upon the 
lines but incompletely represent the characters of the 
stresses. However, if the arrow-heads have been marked 
in accordance with the instructions given in preceding 
articles, the single arrow-head marked upon a line will indi- 
cate the character of the stress. By measuring 8-9 with 
the same scale used to lay off 1-2, and noticing the direction 
of the arrow-head marked upon it, it is found to represent 
a tensile stress of 27,490 pounds. 

In Fig. 270 is represented the truss with joints c’ and 0’ 
loaded, and the joints 6 and ¢ unloaded; also the stress dia- 
gram for this condition, giving the maximum stresses in 
Crceand Gc. 


702 ANALYSIS OF STRESSES. 


As no external forces act upon the truss between A, and 
W,, the entire external space between) these forces is dis- 
tinguished by the same numeral. Likewise, as no force is 
acting in the member P 8, the entire space between the 
members 4a and # ¢ is designated by the same numeral. 
18 + 36 

90 


For this condition of load, A,= 16,200 xX —~——= 9,720 














Scale 1210000 lbs. 


1 9 11 

Fic. 27 
pounds; it is represented by the line 1-2, and the polygon 
1-2-7-1 1s completed for joint a. As there is no stress in 
B 6, 1-7-9-1 is the force polygon for joint 4; 9-7-2-10-9 is the 
polygon for joint c; and 1-9-10-11-1 the polygon for joint C. 
The stress in Cc is represented by 9-10 = + 9,720 pounds, 
and: thatin C ¢c’ 1s represented ‘by 20-17 ==43;750" pounds: 
both stresses are maximum. 

In Fig. 271, the truss is represented with only joint J’ 
loaded. This condition gives the maximum positive shear 
in the panel c’ 0’; that is, it gives the maximum stress that 
could-be produced by the left reaction in a counter having 
the position C'd'. This stress is found in order to determine 
whether a counter is required in this panel. 
18 16,200 _ 


F his load, A, = 
or this load, 7oo== 16,2 200 X a5 = 5 





3,240 pounds. 


ANALYSIS OF STRESSES. 703 


Commencing with 7-2, laid off equal to &,, the polygon 
ee-7-1 15 completed for joint a. ‘For joint 4, 7-7-9-1 
is the polygon; 9-7-2-10-9 is the polygon for joint c; 
-G-10-11-1, for joint C;. 21-10-2-72-1/, for joint ¢; and 
i-fi-i2-Je-]; the .polygon for joint’ Cc’. The line 12-173 = 
— 4,580 pounds represents the maximum stress that could 
be caused in a member C’JO’' by the left reaction. The 





9 11 13 


—_ 


Scale 1£=5000Lbs. 
ite, Carat. 


stress in C’c’ from this condition can not be as great as 
tratround10r Gy in’ the-diagram.of Fio..270* and as Cc" 
bears the same relation to the right reaction as Cc does 
to the left, it will have the same maximum stress. But, 
as previously stated, when the two ends of the truss are 
alike, only those stresses caused by the left reaction are 
obtained; as the maximum stress in C’'c' is caused by the 
right reaction, it is not obtained. 

The maximum live load stresses have now all been found 
The maximum live load web stresses are: 


Stress in B c = — 27,490 lb. 
C ¢ seb 9:720.Ib: 
Gree eb Ost: 
C’.o' = —- 4,580 Ib, 


704 ANALYSIS OF STRESSES. 


It is evident that Figs. 269, 270, and 271 could have been 
combined in one figure. How to do this will be explained 
later. 


1296. It will be noticed that in the stress diagram of 
Pig: 271, 21212 = 9-10, J-2 =e | InCemin Athiszeonaicren 
of load there are no external forces (loads) applied between 
a and 0’, the vertical shear in all panels between these points 
is uniform, equal to &,, and positive. The student will 
notice particularly the fact that the shear in all panels at 
the left of 6’ equals &,. The same would be true with any 
number of loads at the right of any given point, provided 
there were no loads at the left, 1. e., between the given point 
and &,. This shear is positive; that is, if at any point the 
truss be conceived to be cut by a vertical plane, the direction 
of the force on the left of the plane will be upwards, and of 
that on the right will be downwards. ‘This will be referred 
to again. 


THE DEAD LOAD. 


1297. In order to satisfactorily decide the amount of 
dead load to be assumed for a structure, a certain amount of 
previous experience is very essential, if not really indis- 
pensable. As the stresses must be determined, the material 
proportioned, and an estimate of the weight of the structure 
be made before the amount of dead load is known, it is evi- 
dent that the assumption of the dead load must be based 
largely on judgment and past experience. It is very desir- 
able that the assumed dead load may represent, as nearly as 
possible, the actual weight of the structure. If it isassumed 
too light, the structure will not be strong enough; if too 
heavy, material will be wasted. . In either case, if the error 
is considerable, it will be necessary to correct the dead load 
and repeat the operations. 

It is a not uncommon practice among bridge engineers to 
consider 400 pounds per lineal foot as the minimum allow- 
able dead load for bridges; and for very light structures of 
short span, in which the estimated dead load is very light, 


ANALYSIS OF STRESSES. 705 


to never use less than this amount. This practice will here 
be followed. 


1298. Owing to the various forms of floor, differing 
requirements of specifications, and varying conditions affect- 
ing the dead load, no general and satisfactory formula has 
yet been obtained for it. Indeed, it is extremely doubtful 
whether the many and varying conditions upon which the 
amount of dead load depends can be so formulated as to give 
satisfactory results. It is desirable, however, that the 
student be guided by a general formula in assuming the 
dead loads. The following empirical formulas, although but 
roughly approximate, are useful as guides in assuming the 
dead loads of ordinary truss bridges. 

For a capacity of 100 pounds per square foot, 





Dime Sata bb = eh er ead Ht ae (90.) 


For a capacity of 80 pn i square foot, 


w= s+ 5b4o oem ets (91.) 


In both formulas, zw is ay dead load per lineal foot exclu- 
sive of the floor and joists, s is a quantity which will here be 
taken equal to the amount of live load per square foot, 6 is 
the clear width of roadway, and /is the length of span. In 
formula 90,5 = 100; informula91,s5= 80. For any other 
live load capacity s’, find w by formula 90, remembering 
Hiner OUecallsthe required, déad load w.., phen, 


| 
Soak [1 ple EE ] (100—s’).  (92.) 


These formulas have been derived from actual practice; 
when the results obtained by them are added to the esti- 
mated weight of floor, the resulting dead loads will ap- 
proximate reasonably near to the actual loads for highway 
bridges of ordinary dimension and the usual type of con- 
Pp LUGuiOname itereas some experiences tne formulas can ‘be 
adapted to special forms of construction by medifying the 
values of s. 





706 ANALYSIS OF STRESSES. 


The student must bear in mind that these formulas are 
given for convenience and the purposes of instruction only ; 
thev are not to be relied pon in) practice furthersthane to 
afford reasonable checks. 


1299. Having ascertained the kind of floor to be used, 
the weight of floor and joists must be separately calculated 
and added to the results obtained from the preceding for- 
mulas. For ordinary plank floors, supported on timber joists, 
the student may obtain the weight from the following table, 
which has been calculated for the three varieties of timber 
most commonly used: 


TABLE 29. 


Weight, in Pounds per Lineal Foot, of Timber Bridge 
Floor, Consisting of 8" Floor Plank, two 4" x 6" Wheel 
Guards, and the Required Stringers. 
































Yellow Pine. White Oak. White Pine. 
Length r : en 
of Panel) POF Io rece | Seal aratey 1 ano 
in Feet. |» ad. Additional met Additional ween Additional 
way. | Width, | ay, | Width. a Width, 
Add Add Add 
12 peas 36.4 .1262.0 felis LO. 22.5 
13 245 20) «B64 8276.01 AO. Ge lola yas meee 
14 258.8 Bowe 292.8 43 .2 l6i235 23.8 
15 274.5 40.8 292.8 43.2 TOts3 Pan ie e! 
16 2742 5) ) 4025 PB09S6u sd S06) 117 Teg hae 
L750 894051 4 A0VS 180908: OA e Ge Dee ee 
18 290.3 42.8 309.6 45.6 LSdici WeeG ma 
19 290.3 42.8 329.2 48.4 
20 290.3 42. 348 .8 j1.2 


22 327.0} 48.0 





By substituting the proper value in formula 9O, the 
weight per lineal foot of the structure under consideration, 


ANALYSIS OF STRESSES. 707 


(18 —6)90 , 90? 


exclusive of floor, is 100+ 5 x 18 + a Gia 
c oO 


Bd2 





pounds. 

The floor will be assumed to consist of long leaf yellow 
pine. From Table 29, this is found to weigh, for 18 feet 
panel length, 290.3+ 3 x 42.8 = 418.7 pounds per lineal 
foot. The total weight per lineal foot of the structure will, 
therefore, be 352+ 418.7 = 770.7 pounds. The dead load 
will be taken at 770 pounds per lineal foot. As this load is 
considered to be uniformly distributed over the entire 


8 
structure, the panel dead load will be eee el = 





6,930 


7 


pounds. 


THE DEAD LOAD STRESSES. 


1300. The dead load is considered to be concentrated 
at the jointsof the truss. A common practice is to assume 
each panel dead load to be divided between the upper and 
lower chord joints of each panel. In an ordinary through 
bridge with plank floor, it is approximately correct to con- 
sider two-thirds of each panel load to be concentrated at 
the lower, and one-third at the upper chord joint. 

The same results are arrived at in a somewhat simpler 
manner by the following 


Rule.—Odtain the dead load stresses by considering the 
entire dead load to be concentrated at the lower chord joints, 
denoting compression by the + sign, and tenston by the — 
sign , correct the stress thus obtained for each vertical mem- 
ber, by adding to tt algebraically a compressive stress cqual to 
one-third of the panel load. 

This practice will here be followed; it has the advantage 
of giving a stress diagram similar in every respect to that 
for the live load chord stresses, as the conditions assumed in 
each case are the same. For, as the weight of the structure 
is always present in the structure, it is evident that, in 
obtaining the dead load stresses, the truss must be considered 
to be always fully loaded with its dead load. Therefore, the 
stress obtained for any member from the stress diagram for 


708 ANALYSIS OF STRESSES. 


the dead load may be checked by multiplying the corre. 
sponding stress, obtained from the stress diagram for the full 
ave load, by the dead load per lineal foot, and dividing the 
product by the live load per lineal foot. Or, by reversing 
the process, the live load stresses for the chords and end 
posts may be obtained from the corresponding dead load 
stresses. 


Note.—As a low-truss bridge carries no horizontal bracing between 
the upper chords, the error due to assuming the entire dead load to be 
concentrated at the joint of the lower chord is very small, and may 
be entirely neglected. Therefore, for low-truss bridges the entire 
dead load will be assumed to be carrted at the joints of the lower 
chord, and the dead load stresses in the vertical members will not be 
corrected for the error due to thts assumption. 


1301... By formula 89, the dead load reaction R, = 


6,930 X (5 — 1) = 13,860 pounds. In Fig. 272 is represented 









Scale 1=10000 lbs. 





FIG. 272. 


a diagram of the truss and that portion of the stress diagram 
for the dead load which refers to the left reaction: it is in 
every respect similar to the upper half of the stress diagram 


ANALYSIS OF STRESSES. 709 


in Fig 268. It will require no special explanation; the 
lines are drawn in the same order as in Fig. 268. The fol- 
lowing stresses are obtained: 


Stress ina 5 = 1-7 = + 19,600 Ib. 
stress in B A’= 1-9 = + 20,790 lb. 
MIUresceitla.d pes 2 ayee to BGO) ID. 
Stress in’ 2 ¢ = 3-5 = — 13,860 Ib. 
DLressilie are 214-9 =.= 207790: Ib. 
Wiressan ee —7-6.=— — -67930 Ib: 
miresaan 0 a = 5-9) ===" 9. 800:1b, 
SUE Tha 8 UA aime Le eee 0,000 Ib. 


The above stresses may be obtained or checked from 
those determined by the stress diagram of Fig. 268, by mul- 


Hang ; 770 attr: 
tiplying the latter stresses by the quantity aca which is 


the ratio of the dead load to the live load per foot of length. 
The stress for 6 6 is found to equal one panel load, or 
— 6,939 Ib.; to this is to be added algebraically a com- 
pressive stress equal to one-third panel load, or + 2,310 Ib. 
Therefore, the correct dead load stress in & 6 is — 6,930 + 
2,310 = — 4,620 lb. One-third panel load is also to be added 
to the stress obtained for Cc; as the stress diagram gave no 
stress for this member, the correct dead load stress may be 
taken at one-third panel load, or + 2,310 Ib. 


COUNTER STRESSES. 


1302. The effect’ of the dead load reaction has been 
entirely taken up by the loads at dandc, as explained for the 
full live load (Art. 1293), and there is no dead load shear 
in the center panelcc’. It was also explained that, with a 
full uniform load, the effect of the shear is the same as 
though all panel loads at the right of the center were sup- 
ported by the right reaction. As the dead load is a uniform 
load; it is evident that in the panel c’ 6’ there exists at all 
times a negative shear equal to the panel dead load at c’, 
or 6,930 pounds, which is being transferred to the right 
Peactionwes DhiS:)issoreater  thanethe (positive, shear sof 


710 ANALYSIS OF STRESSES. 


3,240 pounds produced in the same panel by a panel live 
load at 6’. (Art. 1295.) It is thus found that no resultant 
positive shear can occur in this panel, and, therefore, no 
counter C’ 0' is required to resist it. The following principles 
are important: 


(a) The maximum live load positive shear in any panel of 
a truss 1s equal to the left reaction when all the joints at the 
right of the panel are loaded and all joints at the left of it 
are unloaded. 


(6) The dead load negative shear in any panel at the right 
of the center 1s equal to the amount of dead load between the 
panel and the center of the span (including a half-panel load 
at the center tf the truss has an even number of panels). 

(c) No counter ts required in any panel beyond the center of 
the truss in which the dead load negative shear exceeds the 
maximum live load positive shear; but in cach panel beyond 
the center in which the live load positive shear can exceed the 
dead load negative shear, a counter ts required. 

The latter principle may be better understood from the 
following considerations: If S is the dead load shear in any 
panel at the right of the center (negative with respect to the 
left reaction), and FR, is the maximum live load positive 
shear in the same (sce (a) above), then the resultant shear 
in the panel will be the algebraic sum of these two shears, or 
R,+S, the value of S being negative. If this sum is 
negative, that is, if AK, is numerically less than S, the re- 
sultant shear will be of the same character as S, and the 
stress induced by it in any member will be of the same kind 
as that induced by-the dead load. In this case, then, the 
diagonal member in the panel is designed to withstand 
either compression or tension alone, according as it may be 
a brace or a tie. But if A, is numerically greater than 
S, then the resultant shear &, + S will be positive, that is, 
of a character the same as X, and opposite to S. In this 
case, Consequently, the member must be designed to with- 
stand stresses of both kinds (one induced by S when the 
truss is unloaded or fully loaded, and one of opposite kind 


ANALYSIS OF STRESSES. ALY 


induced by the resultant of R,+S when the truss is 
partly loaded), or else a new member (counter) must be 
introduced to withstand the resultant shear A,+ S from a 
partial load. 

The student should clearly understand the principles 
stated above. The subject of counter stresses, though 
‘simple, is usually found rather troublesome until it is 
thoroughly comprehended. For clearness the principle will 
be repeated. 


(2) A counter stress will obtain and a counter will be re- 
guired in any panel at the right of the center of a truss when, 
with no live loads at the left of the panel, the left reaction, 
due to live loads at the right, 1s greater than the amount of 
dead load between the panel in question and the center of the 
truss (including a half-panel dead load at the center tf the 
truss contains an even number of panels). 


WIND STRESSES. 


1303. Bridge specifications differ somewhat in regard 
to the amount of wind load necessary to be provided for, 
the most common requirements varying from 100 to 
150 pounds per lineal foot for the unloaded chord, and 
from 250 to 300 pounds per lineal foot for the loaded chord. 
Although a total wind load of 450 pounds per lineal foot is 
rather large for a highway bridge in the ordinary location, 
it will here be used. Throughout the following articles, and 
in the questions referring to them, a lateral wind force of 
150 pounds per lineal foot will be assumed for the unloaded 
chord, and 300 pounds per lineal foot for the loaded chord. 
Of the latter, 150 pounds is to be treated as live load, and 
150 pounds as dead load. The wind load upon the unloaded 
chord will be treated as dead load. 


1304. Dead Wind Stresses in Lower Lateral 
System.—In the example, then, the total panel load of 
wind load for the lower chord is 300 x 18 =5,400 pounds 
(Art. 1289); but of this, one-half, or 2,700 pounds, is to be 


712 ANALYSIS OF STRESSES. 


treated as live load, and the same amount is to be treated as 
f d5—1._. 

dead load. For the wind dead load &, = Pays <x 2;700 Ib. 

= 5,400 Ib. 

The ‘‘ depth of truss” for the lateral systems ts the width 
of the structure from center to center of chords. In the pres- 
ent case, as the chords are one foot in width, the width of 
the structure, center to center of chords, is 18 4+4X 2=— 








9 Scale 1=5000 lbs. 











FIG. 273. 


19 ft. A diagram of the lower lateral system, together with 
a stress diagram for the wind dead load, is represented in 
Fig. 273. 


The force of the wind is assumed to be exerted against 
the windward joints J, c, c', and 0’. As the diagonals are 


ANALYSIS OF STRESSES. 713 


designed to resist tension only, it is evident that but one 
diagonal in each panel acts with the wind against this side 
of the truss, the opposite diagonals acting only when the 
wind force is exerted from the opposite direction, or against 
the joints 0,, c,, c,, and 6,. Asin the main truss, the diag- 
onals in the center panel are not caused to act by the dead 
_load. The members which do not act under the assumed 
conditions are, in the figure, represented by dotted lines. It 
is evident that the reactions R, and RX, can not cause stress 
in the members a, 0, and 6, a,, being exerted in directions 
perpendicular to those members. The members a a, and 
a' a, simply transfer the reactions from the joints a, and a, 
to the joints a@anda’. Indeed, the left reaction may be re- 
sisted in equal amounts by the anchorage at a and at a@,; or 
it may be resisted entirely by the anchorage at a. The 
same is true of the right reaction. When shoe struts are 
used between the anchorages, it is customary to assume that 
the total reaction at each end of the bridge from the wind 
load is divided in equal parts between the two anchorages. 
For the purposes of the stress diagram, however, it will make 
no difference whether the reactions be assumed to be applied 
at the leeward or at the windward anchorages, or divided 
between the two; the total amount of each reaction and its 
line of action will remain the same. 

In the diagram of the truss the reactions are represented 
as though applied at a, and a,; it is evident that under such 
condition the compression in aa, and ina’a,is equal to RX, 
and X,, respectively. The stress diagram is drawn as though 
the reactions were applied at @ and a’. 

In the truss of a lateral system, the positions of the 
external forces correspond to those of a deck truss; the 
stress diagram for the lateral system will, therefore, also 
serve as an example of a stress diagram for a deck bridge. 

In order that the load line may be upon the left side of 
the stress diagram, the external forces are laid off in order, 
beginning with AX, and passing to the /e/¢ around the truss; 
that is, the external forces 1-2, 2-3, 3-4, 4-5, 5-6, and 6-1 are 
laid off in order, passing around the truss in a direction 


714 ANALYSIS OF STRESSES. 


opposite to the movement of the hands of a watch. The 
lower half of the diagram represents the stress due to the 
left reaction, and the upper half represents those due to 
the right reaction. If the external forces were taken in the © 
opposite order, passing to the right around the truss, the 
system of notation would require the stress diagram to be 
upon the left of the load line. 

The student has become so familiar with the construction 
of the stress diagram that it will be unnecessary to explain 
the operation in detail. 

The following stresses are obtained for the members in_ 
the left half of the lower lateral truss: 


stress in a 6 = 1-7, = 5,120 Ib. 
Stress inf c= 6-2 ear OD. 


Stress in 0, ¢, = 2-8 = — 5,120 Ib. 
SLLESS iN Cae = al en a Gy a: 
Stress ina 6,=2-7 = — 17,440 Ib. 
Stress in 6 6,=7-8 =-+ 5,400 Ib. 
Stress 100) 0) 36-9 ee Br 20 LD. 


Stress in¢ ¢, = 9-10 = + 2,700 Ib. 


1305. Live Wind Stresses in Lower Lateral 
System.—For the live wind load, the panel load is the same 
as for the dead wind load. For the members a 0, and 0 0, 
(Fig. 273), the maximum stresses occur when the joint 6 
and all joints at the right are loaded; that is, when the 
truss is fully loaded, or under the same condition as that for 
which the dead wind load stresses were found. Therefore, 
the live wind load stresses for a 6, and 6 6, are the same as 
the dead wind load stresses for the same members. The 
same is true of the live wind load stresses for the chords. 


1306. An essential difference between the deck truss 
and the through truss will now be noticed. If the truss 
were a through truss supporting its loads at the lower chord 
joints, this condition of load (1. e., with all joints loaded) 
would give the maximum stress for a 0,, but wot for 0 0, as 
in the present case; in a through truss, the member 0 0, 


ANALYSIS OF STRESSES. 715 


would obtain its maximum stress with all joints except 6, 
loaded. 

Lach compression web member in a deck bridge and each 
tenston web member in a through bridge receives its maxt- 
mum stress when all joints at the right (including the joint at 
which the member connects) are loaded, no joint at the left of 
wt being loaded. This condition of load also produces the 
maximum stress (of the opposite character) in the member 
which connects with the above member tn the unloaded chord. 
(See Art. 1295.) 

For the maximum stresses in the members dc, andcc,, 
the joint 6 must be unloaded, and the joints c, c’ and 0’ 
remain loaded. For this condition of load, 2, = 2,700 X 
54-+ 36-4 18 


Ee Ib. 
- 3,240 


1307. A diagram of the truss and that portion of the 


stress diagram necessary for determining the stresses in 0c, 
’ | | 








Scale 1'= 5000 Lbs, 


FIG. 274. 
andcc, are represented in Fig. 274. From the latter, the 
stresses in Oc, and cc, are found to be 4,460 pounds and 
8,240 pounds, respectively. These stresses are maximum 
for these members. The stress diagram will be readily 


understood. 
one. 


716 ANALYSIS OF STRESSES. 


For the maximum stress in ¢ c,, the joints 6 and c must be 
unloaded and the joints c’ and 0’ be loaded. For this con- 
36 : 
i = 1,620 lb. Fig. 2% 
shows the diagrams for this condition; the stress diagram 


dition of load, &, = 2,700. x 





2 8 10 
Scale 1=2000lbs. 
1 7 9 ay 
FIG. 27 


will be readily understood. The stress in ¢ c,, which is 
maximum with this load, is found to be 2,230 paanda 

For all members at the right of the center, the stresses 
due to the right reaction will be identical with those which 
have been found for the members at the left of the center. 
Therefore, the maximum stress for ¢’ c, will be greater than 
that given by this condition of load. Atso, for those mem- 
bers which receive stress when the force of the wind is ex- 
erted from the opposite direction, the stress in each is of the 
same respective amount and character as found for the cor- 
responding member above. Xs sthese -membpersmarean] 
opposite diagonals in the panels, they will act as counters for 
the direction at present assumed for the wind. When a 
diagonal acts as a counter, the stress in it is less than when 
‘t acts as a main tie, and, therefore, no counter stresses need 


ANALYSIS OF STRESSES. rol lye 


be found for the lateral system beyond the center panel. 
The maximum live wind stress for each member, as found 
above, must be added to the dead load wind stress, previously 
found, for the same. For the chords and for the members 
in the end panel, the live wind stresses are the same as the 
corresponding dead wind stresses, and the latter may be 
simply doubled. It is evident that Figs. 274 and 275 could 
have been combined. 


1308. Wind Stresses in the Upper Lateral Sys- 
tem.—The upper lateral system will be treated as a truss 
of three panels sup- 
ported at the portals, 
the reactions being 
applied at the latter. 
The panel load is the 
same as the panel 
dead load for the 
lower lateral system, 
Ee ee ee (OUI 


2 = ==2,700 lb. Fig. 








276 is a diagram of 
the upper lateral sys- 
tem with a complete 
stress diagram for 
the wind stresses in 1 ls 

the same. FIG. 276. 

The stresses in & C,and C C\are found to be 3,720 pounds 
and 2,700 pounds, respectively. No stress is found for the 
fiatonalssinethe? Center panels. Dheestress-in® each: of the 
members 5 C, CC’, and C, C, is equal to 2,560 pounds. 


6 Scale 1=5000 Lbs. 


Notrre.—The student, having progressed thus far in the analysis of 
stresses, will probably have become able to readily recognize the char- 
acter of each stress; therefore, the arrow-heads, which have been em- 
ployed to distinguish the characters of the stresses, will be omitted in 
subsequent stress diagrams. Should the student be in doubt, however, 
as to the character of any stress, he should always resort to the sys- 
tem of marking the arrow-heads upon the lines of the stress diagram, 
as explained in former articles, 


718 ANALYSIS OF STRESSES. 


STRESSES IN A LATTICED PORTAL. 


1309. The portal bracing extends across each end of 
the bridge between the upper portion of each pair of end 
posts; it serves to hold the trusses ina vertical position, and 
resists the lateral force of the wind against the side of the 
truss. Through the medium of the upper lateral system, 
the portal bracing, and the end posts, the wind pressure 
against the upper chords is transferred to, and finally resisted 
by, the anchorage at the bottoms of the end posts. In 
the present case, it has been foundthat the amount of wind 
pressure transmitted to each portal by the upper lateral 
system equals 2,700 pounds. 

To this must be added the panel load of wind pressure 
against the ends of the chords and upper portions of the end 


2700 & 


g 





2700 


FIG. 277 (a). 


posts, which is assumed to be applied directly at the portal, 
in equal portions on the windward and leeward sides. ‘This 
is shown in Fig. 277 (@), in which are represented the upper 
lateral system, the portal bracing, and the end posts, together 
with the assumed positions of the wind forces. In Fig. 277 
(0) are represented in outline the portal bracing and the 
end posts, together with the directions and positions of the 
external wind forces acting upon the same. 

The forces are considered to be acting zz the plane of the 
end posts. ‘The dimensions given for the portal bracing are 
the effective dimensions; they are really approximate, but 
they are sufficiently near to the actual dimensions for the pur- 
poses of computing the stresses. The length of the end post. 


ANALYSIS OF STRESSES. eLo 


from center to center of pins, is 25’ 53”; but, asthe upper 
flange of the portal connects on top of the upper chord, for 
the purpose of computing the portal stresses the length of 
the end post will be considered to be 26 feet. The lateral 
wind pressure is assumed to be resisted in equal amounts by 
the anchorage at the foot of each end post, which assumption 
is probably very nearly correct. 

Therefore, in the determination of the wind stresses in the 


2700 
1350 1350 








I Gee oince)s 


portal bracing the following assumptions will be made, when 
not otherwise specially stated: 


(2) When the calculated length of the end post contains a 
fraction, the fraction ts to be taken equal to one foot. 


(0) A panel load of wind pressure (or more, in certain cases, 
as will be hereafter noticed) will be assumed to be applicd 
dircctly against the portal, one-half upon the windward and 
one-half upon the leeward side. 


(c) The total wind pressure at the portal (including that 
applied directly at the portal and that delivered against it by 


720 ANALYSIS OF STRESSES. 


the lateral system) will be assumed to be resisted tn equat 
parts by the horizontal reaction at the bottom of the end posts ; 
z. ¢., the horizontal reaction at the foot of each end post will 
be assumed to equal one-half the total wind pressure against 
the portal. 


1310. The force of the wind against the portal causes 
a downward pressure at @,, the foot of the leeward end post, 
which is resisted by a corresponding upward reaction at the 
same point; 1t also causes an uplifting tendency at a, the 
foot of the windward end post, which is resisted by a cor- 
responding downward, ‘or negative, reaction at the same 
point. These reactions are not vertical except when the end 
posts are vertical; they always have the same directions as the 
end posts. The vertical components of these reactions are the 
vertical supports, or external forces, at the bottom of the end 
posts, but their horizontal components are internal forces or 
stresses in the chords which connect at these points. In 
order to distinguish them more clearly from the laterally 
horizontal reactions, these reactions, though really inclined, 
will be called vertical reactions; they are necessarily rep- 
resented as vertical in the figure. The amounts of these 
reactions and the wind stresses in all portions of the portal 
bracing may be computed by resorting to the principles of 
moments. The vertical pressure at the foot of either end 
post is found by taking moments about the foot of the other 
end post. The total wind pressure against the portal is 
2,700 + 1,350 + 1,350 = 5,400 lb. The moment of this force 
about the foot of either end post must be balanced by the 
moment of the vertical reaction at the foot of the opposite 
end post about the same point; or, calling the wind 
pressure Pand the reaction FR, 26 P—19R = 0, the moment 
of P being positive and that of R being negative. Therefore, 


6 5,4 
LOLA 26iPsandias.4 — 6 40040 ve Ce aid oe 


Ib. (It will be near enough to call this reaction 7,390 
pounds; in the following computations the results will be 
given to the nearest pound.) All the external forces acting 


ANALYSIS OF STRESSES. 1 


upon the portal bracing and end posts have now been deter- 
mined. The magnitude and position of each is shown in 
Big. 277% (0). 


1311. In order to determine the bending moment at 
any point in the portal it is only necessary to find the 
resultant moment of all the forces at the left about the 
point. Each bending moment thus found must be resisted 
by the moment of the internal force in the portal about 
the same point. Therefore, at any point, the moment of 
the internal forces must equal the bending moment at the 
same point; and, if the latter be divided by the lever arm 
of the resisting moment, the quotient will be the magnitude 
of the resisting force, or stress. 

Fig. 278 is a diagram of the portal bracing with some 
dimensions exaggerated and the lattice bars omitted. Upon 
it are written, to the nearest ten pounds, the stresses in 
each flange at intervals of one foot along its length; 1. e., at 
the points where the lattice bars connect. ‘Treating the 
portal asa built beam, the bending moments are assumed 
to be entirely resisted by the flanges; the lattice bars resist 
the shear. It is impossible to correctly compute the stresses 
in the latter, on account of the different paths along which 
the applied forces may be transmitted. 

In order to determine the stress at the point a, moments 
are taken about a’. The resultant moment of the external 
forces at the left taken horizontally and vertically about a’, 
distinguishing those moments which tend to cause rotation 
to the right as positive, and those which tend to cause rota- 
tion to the left as negative, is 2,700 x 22+ 4,050 x 4 — 
fo 00 cleo = 04-915 ft.-lbx* This*moment is positives it is 
resisted by the moment of the internal force, or stress, at a, 
and if it be divided by the lever arm of this resistance, 
the quotient will be the amount of the stress. Therefore 
64,515 

4 
It is evident that a positive bending moment at a’, that is, 
a bending moment which tends to cause that portion of the 
portal at the left of a’ to rotate to the right about that 


= 16,129 lb. is the stress in the upper flange at a. 


722 ANALYSIS OF STRESSES. 


point, will cause compressive stress in the upper flange. 











ar —-—~ -—- —-- ———— y'—— - eis 

| . ; | 
PS telat er tay FOr ott. «Caer rel rst Sh ol 

Ssa esis ggarads sis TUS F | 

| soo Se Pw eS Fe WS VY gs a x l 
Spel eee ya Sp a8 eA Sl «ae ees 1 wl Ss! wl ol 

SN! el ON OS omy OS) Si ol SI SL QOS OM | 

4050 Petpet eats: Lye tee Ly me kfc T yas | 


1350 


BS 
4 











ewe ees oe 


FIG, 278, 


Therefore, this stress of 16,129 pounds at a is compression, 
it has the same sign as the bending moment. 


Nore.—It must be discerned that a + sign employed to denote 
positive bending moment is used in a sense entirely different from the 
meaning it has when it is placed before a stress to denote compression. 
In the present case, a positive bending moment will be found to produce 
compression in the upper flange, and a negative moment will produce 
tension in the same; in the lower flange, the opposite will be found to 
be the case. 


Similarly, by taking moments about 0’, the stress at 0 
2,700 K 23 + 4,050 x 3 — 7,390 X 2.5 
3 








1S TOUT) to eDe 


+ 18,592 Ib. 

By taking moments about z’, the stress at 7 is found to be 

) ; 2— F 

2,700 X 24+ ed 2 — 7,390 X 9.5 _ feieaas beh Teathe 
correct value 7,389.47 pounds were used for the vertical 
reaction, instead of 7,390 pounds, the correct stress would 
be found to be + 1,350 Ib. 

By taking moments about 4’, the bending moment at this 
point is found to be 2,700 X 24 + 4,050 xX 2 — 7,390 x 10.5 = 


ANALYSIS OF STRESSES. 23 


— 4,695 ft.-lb. This moment is negative, that is, it tends 
to cause that portion of the portal at the left of #’ to rotate 
to the left about that point. It is evident that this tendency 
produces tensile stress in the upper flange at #, equal to 
4,695 


6 


= ),045. 1D. 


It will be found that the bending moment changes uni- 
formly from maximum positive at the extreme left to maxi- 
mum negative at the extreme right. The stress in the upper 
flange changes in the same manner except where the depth 
of the portal varies. The compressive stress at any point 
at the left of the center, however, will be found to be just 
2,700 pounds greater than the tensile stress at the corre- 
sponding point at the right. This is because the ‘‘ push” of 
the external forces (4,050 pounds) against the left end of this 
flange is 2,700 pounds greater than the corresponding “‘ pull”’ 
of the external force (1,350 pounds) upon the right end. 
This difference of the external forces at the ends of the 
flanges becomes a resultant compression throughout the 
flange, increasing each compressive stress and decreasing 
each tensile stress by a uniform amount. The compressive 
stress in the left end of the flange is resisted by the lattice 
bars in the left half of the portal, an equal amount by each 
bar (except where the depth of portal varies). Near the 
center the compression in the upper flange becomes entirely 
taken up by the lattice bars, and the stress in the flange 
changes to tension, which increases towards the right in the 
same manner as the compression decreases; at the center of 
2, 700 
ss 
amount of change in the stress at each point along the 
flange equals the horizontal component of the stress in 
the lattice bar which attaches at that point. 


the upper flange, the compression is Sede be 


1312. The stress at any point along the lower flange 
is found by taking moments about the point in the upper 
flange vertically above it. No unequal external forces are 
applied against the ends of this flange. The stress at 


024 ANALYSIS OF STRESSES. 


2, 700 
2 
less than, and of the opposite character to, the stress at 
the corresponding point in the upper flange; being zero 
at the center, compression at the right of the center, and 
tension at the left. The bending moment at each point 
has the same sign as the corresponding bending moment 
for the upper flange; but it is evident that a positive bend- 
ing moment at any point (tending to cause that portion 
of the portal at the left of the point to rotate to the right 
about the point), while producing compression in the upper 
flange, would produce stress of the opposite character, or 
tension, in the lower flange. Thus, the stress at 4’, found 
2,100 X 26 — 7,390 X 8.5 
2 
= 3,693 lb.; the bending moment producing this stress is 
positive, but the stress is tension and is given the — sign. 
The bending moment producing the stress at z’, found by 
taking moments about z (using the correct value of the 
vertical reaction), is 2,700 X 26 — 7,389.47 x 9.5 = 0; the 
stress at z is, therefore, zero. Taking moments about &, 
the bending moment is 2,700 X 26 — 7,390 x 10.5 = — 7,395 
ft.-lb. As previously explained, a negative bending moment 
causes tension in the upper flanges; but it causes stress of 
the opposite character, or compression, in the lower flange; 


therefore, the stress at £' 1s set? 3, 605 Ib. The 


= 1,350 pounds numerically 





each point is found to be 





by taking moments about %, equals 


compressive stress in the lower flange is found to increase 
from the center towards the right in precisely the same 
manner that the tensile stress increases towards the left. | 


1313. An:the flanges.of the-brackets -at-thepleiieone 
and at the right of f’, the conditions are slightly changed, 
owing to the fact that the changes in the direction of the 
flange change the lines of action of the internal forces acting 
along the flange. It must be kept in mind that the lever 
arm of a moment must always be taken perpendicular to 
the line of action of the force. For the stress in the lower 


ANALYSIS OF STRESSES. 725 


flange at 4’, moments are taken about 0; the bending 
moment at the latter point is 2,700 X-26 — 7,390 x 2.5= 
51,725 ft.-lb. In order to obtain the stress at 0’, this bend- 
ing moment must be divided by the perpendicular distance 
from the line of action of the stress to the center of rotation 
b, which is the distance 6 6". This distance is approximately 
2.121 feet, and the stress at 0 is Bee = — 24.387 lb. -The 
perpendicular distance 06" may be either calculated or 
measured; instead of finding this distance, however, it is 
usually more expeditious to proceed as follows: 

Find the horizontal component of the stress, that is, find 
the stress as though the flange were horizontal, by dividing 
the bending moment by the vertical lever arm; as 
51,725 
ek 
thus found upon a horizontal line, and project it vertically 
(i..e., parallel to the lever arm | 
used) upon a line drawn parallel 
to the line of action of the desired 
stress; that is, parallel to the 
flange. The operation is shown 
in Fig. 279. By measuring the 
fattet 1ineetoethe scale used, the 
stress in the flange at 0’ is found 
to be + 24,380 lb. 

By applying the known prin- 
ciples of moments and proceeding 
as explained above, no_ special lees, 
difficulty will be encountered in obtaining the stress at each 
point along the flanges of a latticed portal. 





= 17,242 lb. Then, lay off the horizontal component 


irre —17240 lds. ay 





1314. The increment of the flange stress at any point 
is the horizontal component of the combined stress in 
the two lattice bars which connect at that point. If it be 
assumed that the entire increment of the flange stress is 
borne by the lattice bar which is.in tension, then the differ- 
ence in the flange stress at any two points becomes the 


726 ANALYSIS OF STRESSES. 


horizontal component of the stress in the (tension) lattice bar 
which connects at the point having the greater flange stress, 
if tension, or the smaller flange stress, if compression. 

To obtain the stress in the lattice bar, lay off upon a hori- 
zontal line the horizontal component of the stress, found by 
taking the difference 
of the stresses at two 
adjacent points, and 
project the same ver- 
tically dpone lime 
drawn parallel to the 
lattice bar. 

For example, the 
difference bet ween 
the, stressess ataune 
points: % “and: ais 
3,700 pounds. (See 
Pig 250s) ae Lisa 
laid off upon the hori- 
zontal line /’ z’ by any 
convenient scale, and 
the point /' is pro- 
jected vertically upon 
the line 7’ 2’, drawn 
through 2’ parallel to 
thé lattice: bars 7 2 9 The line 2 =) 2e0 ibe cor ceo 
the stress in the lattice bar 7¢ z. 








FIG. 280. 


EXAMPLE FOR PRACTICE. 
Compute, to the nearest ten pounds, the stress in each flange of the 
portal at each point for which the stress is given in Fig. 278. 


FLOOR BEAM STRESSES. 


1315. The floor beams are the members which support 
the floor load and transfer it to the joints of the loaded 
chord. In most bridges the floor beams are small plate 
girders. Therefore, the following explanation of the method 
of obtaining the stresses in a floor beam will also apply to 


ANALYSIS OF STRESSES. T27 


any plate girder carrying a uniform load. Ina bridge hav- 
ing two trusses, the tota!i live load upon a floor beam is twice 
the panel load supported by one truss; in the example the 
amount of live load supported by a floor beam is 16,200 x 
2 = 32,400 lb. 

The weight of the floor plank and joists, as previously 
obtained from Table 29, Art. 1299, is 418.7 pounds per 
lineal foot. Calling this 419 pounds, the weight of floor 
supported by one beam is 419 x 18 = 7,542 Ib. 

The weight of the beam itself may be estimated by the 
— following formula: 

gris gem 

20:2’ 

in which Pis the weight of the beam, W is the total live 
load supported by it, /is the distance in feet between sup- 
ports, and @ is the total depth of the beam in inches. This 
formula apphes to ordinary iron floor beams built of plates 
and angles in the usual form; the results given by it are but 
roughly approximate, but are sufficiently accurate for the 
purposes of computing the stresses. The total live load upon 
the beam has been found to be 32,400 lb. = W. The dis- 
tance between supports is 19 ft.=/. The value of d@ is taken 
at 24.5 inches; the depth of the beam will again be referred 
to further along. By the formula, the approximate weight 
32,400 x 19 
20 X 24.5 


(93.) 


= leo UELD; 





of the beam is 


1316. The total amount of live and dead load sup- 
ported by a floor beam is, therefore, 382,400 + 7,542 + 
15206 = 41,198 Ib., “or say 41,200 ‘pounds. This load ‘is 
assumed to be uniformly distributed over that portion of 
the roadway supported by one beam. Asthe beam carries 
the entire load between its supports, the condition is that of 
a simple beam. The maximum bending moment, which 
occurs at the center, may readily be found by constructing 
the moment diagram, but, as it is a very simple case, it will 
be more expedient to compute it from a formula. 

By applying the principles of moments to a beam carrying 


028 ANALYSIS OF STRESSES. 


a uniform load of cv pounds per foot, the maximum 





ae 
bending moment is found to be J7= “: * OF; SINCE 707 == 
total load = W, we may write, 
m=". (94.) 


1317. For a uniformly loaded beam, the bending 
moment J/, at any point O, situated at a distance x from 
the center, is found by the formula 


WI W x? 


NT Soa ee a 


(95.) 





or, if the weight zw per foot be used, 
wil / 
M, — Q (5 —— +) (5 4. r), (96.) 

The values of the characters used in the preceding 
Poceeen - formulas will be 
| ) clearly understood 

IO iit AA pyitefere nee ieee 
PERS 27; “9 281; O is the point 
Fic. 281. # for which the bend- 
ing moment is given by formulas 95 and 96. 








1318. Formula 94 is commonly used to obtain the 
maximum bending moment for the floor beams of highway 
bridges. As the flanges of such beams are usually made of 
uniform section throughout their length, the maximum 
moment is the only moment necessary to be found. 

Formulas 94, 95, and 96, however, do not correctly ap- 
ply to the floor beams of bridges, as the condition of a load 
distributed uniformly over the length of the beam does not 
obtain in a floor beam, even with the roadway uniformly 
loaded. The floor beam is not uniformly loaded over its 
entire length between supports, for it is supported at the 
centers of the chords, and can be loaded only over that 
central portion of its length corresponding to the clear width 
of roadway. In the present case, the distance between 


ANALYSIS OF STRESSES. 029 


supports is 19 feet, while the clear width of roadway is 18 feet. 
The error arising from applying formula 94 to a floor beam 
is small, but it is an error on the dangerous side, always 
giving a bending moment slightly too small. 

The following is a much better formula for the maximum 
or center bending moment J/ of a floor beam: 


W (6+ 2c) 
8 > 





si (97.) 
in which @ is the clear width of the roadway, and ¢ is the 
width of one chord, while /V represents the same value as 
before. | 

The bending moment J/, at any point O, situated at a 
distance x from the center of a floor beam is given, by the 
formula 





W (6+ 2¢ Wea 
ee (98. 
in which all characters have the same significance as in 
formulas 95 to 97, 
and will be clearly 
die? 6.010 ad) “by 
Peaerencer.tp | Hic: 


282. 
1319. _ Follow- 


ing the usual prac- 
tice for short beams, 
however, the flanges of the floor beams in the example will 
be made of uniform section throughout their entire length; 
and, therefore, for the purpose of determining the required 
section, it will be unnecessary to determine any bending 
moment other than the maximum or center moment, which 
is given by formula97Z. Inthe examplec, the width of each 
upper chord is 1 foot, and, by applying the formula, the 
maximum bending moment is found to be - ee oe 2) == 
103,000 ft.-lb., or 103,000 x 12 = 1,236,000 in.-Ib. 

The lever arm of the resisting moment, which must equal 








FIG. 282. 





730 ANALYSIS OF STRESSES. 


the bending moment, is generally considered to be the dis- 
tance between the centers of gravity of the flanges. For 
ordinary floor beams, it is good practice to make the total 
depth of the beam equal to about one-tenth of the span. This 
depth may be increased or diminished, according as the load 
is heavy or hght, or it may be modified to meet the require- 
ments of other controlling circumstances; the practice is by 
no means to be rigidly followed. In the present case, one- 
tenth the span is ese “ Tas 22.8 in. A web-plate 24 inches 
deep will be used. As the depth of the beam, out to out of 
flange angles, can usually be made from one-quarter to one- 
half inch deeper than the depth of the web-plate, the depth 
of the beam in the present case will be 244 inches. 

In the ordinary sizes of angle bars used for floor beams, 
the distance from the centcr of gravity of the bar to the back 
of the longer or horizontal flange usually approximates % of 
an inch, and may generally be taken at that amount. In the 
present case, then, 24.5 — (.75 X 2) = 23 inches may ‘be 
taken as the distance between the center of gravity of the 
flanges. This is known as the effective depth of the 
beam. 

The maximum bending moment divided by the effective 
depth of thé ‘beam -(1..¢.; the lever varm of the resictme 
moment) will give the maximum resisting force required, or 
flange stress. As the effective depth 1s always expressed in 
inches, the bending moment must be expressed in inch- 
pounds. Inthe example, then, the maximum flange stress is 
ste oo b3, 740 1b 

1320. It is evident that formulas 94 and 97Z may be 
readily made to represent maximum flange stress instead of 
maximum bending moment by simply introducing a quantity 
representing the effective depth of the beam into the de- 
nominator of each. Let d represent the effective depth of 
the beam, and let S,, represent the maximum flange stress. 
Then, from formula 94, . 


ANALYSIS OF STRESSES. ren 


Wl 





Se — os (99.) 
Similarly, from formula 97, 
. _W(b+2c) 
Ses 3a ; (100.) 


1321. The maximum shear in the beam occurs at the 
supports, and is equal to the reaction (half of the load on 
the beam). At any other point the shear equals the re- 
action minus the load between the point and the support. 
In general, the shear atany point of auntformly loaded beam 
equals the load between that point and the center of the beam. 
fied) = oad per toot. shear at. ardistance.of 2 feet from 
center = WwW x. 

7 41,200 

2 


In the example, each reaction equals = 20,600 Ib. 


This is also the maximum shear in the beam, uniform for 
about 6 inches towards the center from each reaction. 


EXAMPLES FOR PRACTICE. 
Note.—Find each result to the nearest hundred pounds. 


1. For the above floor beam, (a) calculate the maximum bending 
moments, in foot-pounds, by formula 94, and (4) reduce it to inch- 
pounds. Ate { (a) 97,850 ft.-lb. 

( (6) 1,174,200 in.-lb. 


2. By formula 95, find the bending moment, in inch-pounds, (a) at 

a distance of 4 feet, and (4) at a distance of 8 feet, from the center 
of the same beam. re § (a) 966,000 in.-lb. 
( (6) 341,500 in.-Ib. 

3. Find, by formula 98, the bending moments, in inch-pounds, for 
the same points in the floor beam. ne (a) 1,016,300 in.-lb. 


(6) 357,100 in.-1b. 


4, Construct a moment diagram for the beam (i. e., for a simple 
beam 19 feet long between supports, carrying a load of 41,200 pounds, 
uniformly distributed over the central 18 feet of its length, leaving 
6 inches between each support and the corresponding end of the load). 
Determine the bending moment in inch-pounds at the center of the 
beam, and at points 4 feet and 8 feet, respectively, from the center, 
ascertaining which of the above results are correct. 


T. IT.—8 


732 ANALYSIS OF STRESSES: 


STRESS SHEETS. 


1322. The maximum stresses in all the main members 
of the structure chosen as an example have now been 
found and each operation has been fully explained. In Fig. 
283 these maximum stresses are shown written along the 
respective members in the left half of a diagram of the truss 


L+48600 L+45600 
D+20800 D+20800 









L-16200 
D-4600 


~~ L-32400 L— 32400 L—48600 
D-13900 D-13900 D-20800 
#10200 +15300 +15300 

Pt 





- 10200 — 15300 
Length of Span, C. to C. End Pins................. = 90'-0" 
Height of Trusses, C. to C. Chord Pins........ .... = 18'=0" 
No. of Panels= 5. Length of Each Panel.......... = 18’ =0" 
Clear Width: Of: ROadWway ern. cs oe sorceress oe ee eee = 18’=0" 
Live: Load per Sq. Picasa: 4 we ee = 100 Ib. 
Live. Loadtper Lin. Ft. 2.cterenes can ecient = 1800 Ib. 
Deadsloadtpern Cin whl. 3.0 penance eee 7K) i fn 
FIG. 283. 


and in a diagram of the lateralsystems. In the latter the left 
half represents one-half of the lower lateral system, while 
one half of the upper lateral system, together with the portal 
bracing, is represented in the right half. The stresses are 
written along the respective members in each. On each 
member in the diagram of the truss the live load stresses and 
dead load stresses are written separately, but in the lateral 
diagrams the live and dead wind stresses for each member 
are combined. The maximum floor-beam stress is written 
in the diagram of the lower lateral system. As the amount 
of stress in the floor beam depends upon the depth of the 
beam, it is necessary to designate the depth of the web plate. 


ANALYSIS OF STRESSES. 133 


The portal stresses are not given. Each stress is written 
correctly to the nearest hundred pounds only. The data for 
the bridge, giving the general dimensions and assumed loads, 
are written below the diagrams. 

such diagrams, with complete data, are usually con- 
structed upon cap size sheets of paper, or larger when 
_ necessary, and are sometimes known as strain sheets; 
the name stress sheets applies more properly, however, 
and will here be used. All stress sheets required to be 
made throughout this Course should, whenever possible, be 
constructed upon sheets of paper of cap size. 

The stress sheet shown in Fig. 283 is incomplete; the 
material for each member, when proportioned, is also to be 
written along it. 


1323. The method of the graphicalanalysis of stresses, 
explained in the preceding pages, 1. e., the method of determ- 
ining the stresses by means of the stress diagram, or combined 
force polygons, constructed for the forces which act upon 
the several joints of the truss, is commonly known as the 
Clerk Maxwell method, being named after Prof. Clerk 
Maxwell, one of the early investigators in graphical statics, 
who largely developed and extended the method. 

It is by no means the only method that can be employed 
for this purpose; but it is probably the best graphical 
method. After becoming familiar with the operations, the 
student will be able to somewhat shorten them. For the 
present, however, and until he has become thoroughly 
familiar with all the processes, it will be better for him to 
systematically follow the method as given. 


METHOD BY THE MOMENT AND SHEAR 
DIAGRAMS. 

1324. A method of obtaining the stresses by means of 
the moment and shear diagrams will now be briefly ncticed. 
The live load stresses will be obtained for the members of the 
truss of the structure which was chosen to illustrate the 
previous method, The construction for the live load stresses, 


734 ANALYSIS OF STRESSES. 


shown in Fig. 284, will sufficiently illustrate the method. A 
diagram of the truss, as a /, is first constructed; through the 
lower chord joints, a, 0, c, d, c, and f lines are drawn verti- 


Scale for Truss: 1 in. = 360 ft. 


yD 








+ 
ss 
ea) 
z= 
" ! b ¢ d e 7 
rare f Rtmercebynd de 3 meters ord hal a ated (eee ef 
| ; 
\y \ | 
a | i | 
| b! | ! 
a | | 
‘ | lan 
| la’ | 
! | ! 
len 
a b ] 





Se ne ig” a ARN cn aT 














Scale for Loads: 1 in. = 32,000 Ib. 
FIG. 284. 


cally downwards. Upon the vertical through a, the panel 
loads are laid off downwards in order, forming the load line. 
Thus, 0-1 = 16,000 pounds represents the panel load at 0; 
1-2, the panel load atc, etc. The scale used for this purpose 


ANALYSIS OF STRESSES. 135 


is not necessarily the same as that used for the diagram 
of the truss. Choose a pole P, and draw the rays of the force 
diagram: P0, Pi, P2, P$,and P4. The position of the pole 
should be so chosen that the pole distance //7 will be some 
convenient multiple (or factor) of the height of truss. In 
the example the height of truss is 18 feet, and the pole dis- 
tance is made equal to 36,000 pounds. . Construct the 
equilibrium polygon, or moment diagram, by drawing lines 
parallel to the rays of the force diagram, in order between 
the verticals through the joints of the truss, and finally the 
closing line f' a’, drawn from /’, the terminus of the last 
line, to the starting point a’. The line Pz, drawn from P 
parallel to the closing line 7’ a’ of the moment diagram 
divides the load line into reactions m 4= R,and #z0= K.,. 


1325. Stresses Due to Bending Moment.—The 
intercept in the moment diagram, ona vertical through any 
joint, measured to the scale used to construct the diagram 
of the truss, when multiplied by the pole distance and 
divided by the height of the truss, will give the chord stress 
in each chord between those two diagonals between which 
the vertical member at that joint is situated. The inter- 
cepts. 2 6° and c’c’ are found to equal 16.2 ft. and 24.3 ft., 
respectively. Calling the height of truss /, 

Pie ea 356,000 

Cot X 7 = 24.3 X i 

is the chord stress in the upper and lower chords between 

the diagonal members Ac and Ad. As the diagonals Cd 

and Yc do not act when the truss is fully loaded, the maxi- 

mum stress in the upper chord is uniform from # to &. 
The intercept 0” 0’ was found to equal 16.2 ft., and 

36,000 

Ret oh 





— 48,600 lb. 


val 
b” b “<= = 16.2 X< 
hh 


is the chord stress in the lower chord members ad and Oc, 
i.e., between the diagonal members a 4 and Le. 


32,400 Ib. 








1326. Stresses Due to Shear.—As the line Pm, 
Fig. 284, drawn parallel to the closing line of the moment 


736 ANALYSIS OF STRESSES. 


diagram, divides the load line 0-4 into the reactions m 4 and 
mO, a horizontal line, drawn through 7z, as the line mm 2, 
becomes the shear axis, and0O gh ...g97 4m, drawn accord- 
ing to the instructions given in Art. 1228, becomes the 
shear line for this load. As this condition of load gives the 
maximum shear in the panela Jd, and, therefore, the maximum 
stress ina /, a line drawn parallel to a 4 between the line 
0 g, produced if necessary, and the shear axis, as the line 


oO) 
mg’, will represent the maximum stress in that member. 


Sey? 

Measured to the scale used in laying off the load line, the 
line wz ¢’ is found to equal 45,800 pounds. 

For the maximum shear in the panel 4c, and the maxi- 
mum stress in the member /c, the panel load at J, repre- 
sented by 0-7, is considered to be removed; /-4 now becomes 
the load line and 7-4-/P-1, the force diagram. The moment 
diagram remains the same as before, except that, as the line 
PO no longer belongs to the force diagram, there is no 
longer any line in the moment diagram parallel to it, but 
the line c’ 0’ continues parallel to P 7 till it intersects the 
vertical through @ata,. The line f’ a, becomes the new 
closing line of the moment diagram; P 7, is drawn parallel 
to f' a,, and m, m, becomes the shear axis for this load, for 
which 1zklopqvr isthe shear line. The left reaction for 
this lead is represented by 7 7, = 19,440 pounds, which line 
also represents the shear at any point between aandc. A 
line drawn between the line z 7 and the shear axis m, n, 
parallel to 4c, as the line % “’, will represent the maximum 
stress in Bc. Measuring with the scale used for the load 
line, 2 /' is found to equal 27,500 pounds. 

For the maximum shear in the panel d, and maximum 
stress in the member C d, the load at c, represented by 1-2, 
is also considered to be removed. For this condition of load, 
2-4-P-2 becomes the force diagram; a, c’ d' e’ f' a,, the 
moment diagram; 7, 2,, the shear axis, and 2/o0pq,r, the 
shear line. On the load line #, 2 = 9,720 pounds, represents 
the left reaction; it is equal to the shear at any point 
between a and dand to the maximum compression in Cc. 
A line & &', drawn parallel to C d between the line 2-1 and 


ANALYSIS OF STRESSES. "3% 


the shear axis m, m,, represents the maximum stress in the 
member d.7- lO the scalésused for the load line? 7,2 = 
9,720 pounds and # &’ = 13,700 pounds. ‘The stress in LO 
is simply tension equal to one panel load = 16,200 pounds. 

The maximum live load stresses have thus been found for 
all members in the left half of the truss; those for the cor- 
responding members in the right half are identical with 
those found. The dead load stresses are found in substan- 
tially the same manner, the truss being considered fully 
loaded. The method will be readily understood from the 
above explanation of the process of finding the live load 
SLLESSES. 

This method, as applied to special cases, can be much 
shortened, but it can not be expeditiously applied to all forms 
of trusses. 


EXAMPLES FOR PRACTICE. 
1. For the same bridge construct the moment and shear diagrams 


for the dead load, determining the dead load stresses. 


2. Construct the moment and shear diagrams determining the live 
wind stresses in the lower lateral system. 


3. Construct the moment and shear diagrams determining the dead 
wind stresses in the same. 


4. Construct the moment and shear diagrams determining the 
wind stresses in the upper lateral system. 


A SHORT METHOD FOR WEB STRESSES. 


1327. The maximum live load web stresses for a truss 
having parallel chords may be obtained by a much shorter 
method than has been previously explained. Such a 
method will now be explained by an example. 

For the truss of a through bridge of 90 feet span, the 
same data will be used that were given in Art. 1292, 
except that the truss will be divided into 6 panels and the 
height of the truss will be 15 feet. The panel length is, 


PieLerare, = = 15 feet, and for one truss the live panel load 


738 ANALYSIS OF STRESSES. 


1:800< 15 
is ——_~——— 


7 


= 13,500 pounds. The dead load will be taken 


at 770 pounds per lineal foot, as obtained in Art. 1299; for 
one truss, therefore, the panel dead load is ue ee = 
5,775 pounds. 

A short method of determining the maximum live load 
stresses is as follows (see Fig. 285). 

Construct a diagram of the truss toa rather large scale. 
From a, the joint at the left reaction, lay off upwards upon 
a. vertical: line the lefts reaction: from -a ‘full load 4as e724. 
This constitutes the load line, upon which from 2’ lay off 
downwards, consecutively, those portions of the several panel 


























e y | g 

eo ue iad _is hake ee pe) ee -15— + 

abso 90 a 

Scale for Loads: 1 in.= 40,000 Ib. 
FIG. 285. 














loads supported by the left reaction, taking the loads in 
order and passing to the right across the truss. R, = 
13,500 (++ 4434244) =11,250+ 9,000+ 6,750.4 4,500 + 
4,200 =00,1D0> 1D... Chen, . tae i. 3) 750 aslowiouiatd melt 
upwards, and 2’-3' = 11,250 lb., 3’-4’ = 9,000-lb., 4'-5’ = 
6,750 ‘Ib., 6-6° = 4,500 1b., and 6-7 = "9 250 Ibaare iad 
off downwards in order to the starting point 7’ or a. Also, 
from I’ lay off upwards upon the load line, or, as in the 
figure, from a point horizontally opposite 7’, lay off upwards 
upon a vertical line 4,-5,, 5,-6,, and 6,-1,, equal, respect- 
ively, to 2,888 Ib., 5,775 lb., and 5,775 lb., the amounts of 
dead load at d, e, and Ff, respectively, that are supported by 
the vzgh¢ reaction. The right reaction due to “ve load is 
entirely neglected. 

Upon the load line, Z'-2’ represents the left reaction 









ANALYSIS OF STRESSES. 739 


due to live load with the truss fully loaded, which condi- 
tion gives the maximum stress in the member a &. Pro- 
ject the point 2’ upon a 4, produced if necessary, by the 
horizontal line 5’ 2’; then, a 4’ will represent the stress in 
ab. The maximum stress in 4c obtains with the load at 0d 
removed, all other joints being loaded. For this condition 
_ 1'-3' represents the reaction, and by projecting the point 
5’ upon / ¢ (also produced, if necessary) by the horizontal 
line J’ 3’, the line 4’ c will represent the stress in Bc. The 
maximum stresses in C ¢ and Cd obtain with the load at 
c also removed, all joints at the right remaining loaded. 
The reaction for this condition is represented by /’-J’, 
and by drawing through 4’ the horizontal line c’ 4’, the line 
C’ ¢ will represent the stress in Cc¢ andc'd will represent 
the stress in C d. The maximum stressesin Ddiand De 
obtain with all loads at the left of the panel @ e (numeral 
5) removed, all joints at the right of it remaining loaded. 
For this condition i'-5’ represents the reaction, and by 
drawing through 34’ the horizontal line d' 5’, the lines D' d 
and @’ e will represent what would be the stresses in ) d@ and 
D ¢, respectively, if no negative dead load shear existed in 
the panel d ¢. The negative shear in this panel is repre- 
sented by 4,-5, and by drawing through 4, the horizontal 
line 2,,-5,, the lines D’ d, and d’ ¢’,, will represent the result- 
ant live load stresses in Dd and De, respectively. With 
the load at e also removed, all joints at the right remaining 
loaded, i’'-6' represents the reaction. This condition will 
give the maximum stress for the member & /, if any stress 
can be found for that member; by drawing through 6’ a 
horizontal line 6’ ¢’, the line ¢’ f will represent what would 
be the live load stress in # /, if no negative shear existed in 
the panele f. But an amount of negative dead load shear 
represented by 4,-6, is always present in this panel; a 
horizontal line 6, 7, drawn through 6, will le above the 
line ¢’ 6’, showing that the ‘negative dead load shear more 
than counteracts the positive live load shear in this panel. 
Therefore, no stress can be obtained for a tie in the posi- 
boveee 7) Lhe maximum stresssin thes vertical member 


vt 


740 ANALYSIS OF STRESSES. 


- ¢ is produced by the right reaction, and is the same as has 
been found for Ce. 

It will be noticed that the dead load numeral 6, is situ- 
ated above the live load numeral 6’, and that wo stress is pro 
duccd by positive shear in the panel e f under which the 
corresponding numeral 6 is situated; also, that the dead- 
load numeral 4, is situated dc/ow the live load numeral 4’, 
and that stress 7s produced by positive shear in the panel 
@e under which the corresponding numeral 4 is situated. 
This will always be the case, and it will always correctly 
indicate whether counter stress will be found in any panel 
of a truss having parallel chords. 


1328. The method of laying off the load line and 
determining in what panel the counter stress ceases may 
be described in a general manner as follows: 


(a) The left reaction due to the live load ts laid off upwards 
upon a vertical line erected at the left support ,; thts consti- 
tutes the load line, the right reaction due to the live load being 
entirely neglected. 

Irom the top of the load line the respective portions of the 
live panel loads which are supported by the left reaction are 
laid off in order downwards, taking the loads from the left to 
the right across the truss, the last load will just reach to the 
bottom of the load line. From this point, or from a point on 
a vertical line horizontally opposite to it, the dead loads, sup- 
ported by the right reaction, are laid off upwards, Be op at 
the center of the truss and passing in order towards the right 
until the numeral used to designate the dead load shall fall at 
a point upon the load line above the corresponding numeral 
employed to designate a live load. 

When this occurs, no positive live load shear will be found 
an that panel of the truss under which the corresponding 
numeral ts situated, nor in any panel to the right of it. But 
positive live load shear and counter stress will be found in 
each panel whose numeralused to designate the live load ts 
situated ata point on the load line above the corresponding 
numeral used to designate the dead load. 


ANALYSIS OF STRESSES. 741 


1329. In determining the web stresses, proceed as 
follows: 


(b) From the point upon the load line indicating the upper 
limit of the reaction for cach condition of load, a horizontal 
line 1s drawn intersecting those web members which obtain 
their maximum stress with that condition. Tf the members 
areat the right of the center of the truss, a horizontal line ts 
also drawn tointersect them from the corresponding. dead load 
numeral, 

On a line representing a member of the truss for which 
the maximum stress obtains in any of the several conditions, 
the portion below the horizontal line drawn from the lve 
load numeral to intersect it (and above the line drawn from 
the corresponding dead load numeral, if the member ts not at 
the left of the center) will represent the stress in the member. 


EXAMPLES FOR PRACTICE. 


1. By the method just explained, find the maximum live load web 
stress for the truss shown in Fig. 285, using the data given. 


Ans. For a & + 47,730 Ib. For C d— 19,090 lb. 
For 2 c — 81,820 lb. For 2) d+ 3,860 lb. 
For C ¢+ 13,500 Ib. For D e — -5,460 lb. 


2. By the same method obtain the maximum live load web stresses 
for the five panel truss of the previous articles. 


THE HOWE TRUSS. 


1330. The earliest form of simple truss of any consid- 
erable length of span that was built for bridge purposes in 
America is shown in Fig. 286. It was devised by William 


a = as ——/. ~ wt a ee, 





saeaese Roscnaeuseaneh 
ae 


rpstseeeeeseseeeees - 
nee . 
one 4 











FIG. 286. 


Howe, in 1840, and is known as the Howe truss. It isa 
very excellent form of truss, and is still much used in this 
country in localities where timber is cheap. For trusses 


742 ANALYSIS OF STRESSES. 


constructed entirely of metal, however, it is not as economi- 
cal as the Pratt truss. 

In the Howe truss all vertical members (except end posts) 
are tension members, and all diagonal members in the web 
system are compression members. 

As originally constructed, the Howe truss had short 
panels with two diagonal braces in each panel, and vertical 
end posts; the floor was supported directly upon the lower 
chord, which, therefore, acted as a beam as well as a tension 
member. All parts of the truss were constructed of wood 
except the intermediate vertical members, which were 
iron rods. It is evident that the members represented in 
the figure by dotted lines can carry no stress; they serve no 
other purpose than to stiffen the truss. 


1331. In modern examples of the Howe truss, those 
members which do not bear stress are omitted, and the lower 
chord is usually constructed of metal. Such a truss for a 
through bridge is represented in Fig. 287. For the sake of 





FIG. 287. 


comparison, the same data are assumed for this truss that 
were assumed for the Pratt truss, treated in the preceding 
pages; namely, length of span, 90 ft.; panel length, 18 ft. ; 
height of truss, 18 ft.; clear roadway, 18 ft.; live load, 
1,800 Ib., and dead load, 770 lb. per lineal foot. 

The Howe truss, of Fig. 287, is very similar to the Pratt 
truss, shown in the previous figures; the essential difference 
is that in the former all vertical members are ties and all 
diagonal members are struts, while in the latter the oppo- 
site is the case. It will be noticed that in the Howe truss 
the hip vertical is not merely an independent suspender, as" 


ANALYSIS OF STRESSES. 743 


in the Pratt truss, but is an important part of the entire 
web system; the amount of shear resisted by it is the same 
as that resisted by the end brace. 

The method of constructing the stress diagram is substan- 
tially the same for both trusses, and after what has been ex- 
plained concerning the Pratt truss, no difficulty will be en- 
countered in obtaining the stresses for the members of the 
Howe truss. It must be noticed that, as in this truss the 
duties of diagonal and vertical members are the reverse of 
what they are in the Pratt truss, the maximum stress in any 
vertical web member of a Howe truss, and in the diagonal 
meeting tt at the upper chord, occur when the joint at the 
foot of the vertical member and all the joints at the right are 
loaded, the others being unloaded. 

(In the solution of Question 595, the student has drawn 
the stress diagram for a four-panel Howe truss carrying a 
full uniform load.) 


EXAMPLES FOR PRACTICE. 


1. Construct the stress diagram obtaining the dead load stress in 
each member in the left half of the truss shown in Fig. 287, using the 
data given above and correcting the stress in each vertical member. 


Ans. For a & + 19,600 lb. For ¢ c’ — 20,790 Ib. 
For & C.+ 18,860 Ib. For 2 6 — 11,550 Ib. 
For CC" + 20,790 lb. For 6 C+ 9,800 lb. 
For a &— 13,860 lb. For C c— 4,620 lb. 


For 6 ¢c— 20,790 lb. 


2. Compute the live load stresses in the chords and end posts from 
the corresponding stresses obtained in the solution of the preceding 
example. 


Ans. For a £& + 45,820 lb. For a 6 — 82,400 lb. 
For B C + 82,400 lb. For J c — 48,600 lb. 
For CC’ + 48,600 lb. For cc’ — 48,600 lb. 


3. Construct the diagrams for the maximum live load web stresses. 

Ans. For B 6 — 82,400 lb. 

For 6 C + 27,490 1b. 

For Cc — 19,440 lb. 

For ¢ C' + 138,750 lb. 

4. Solve the above example by means of the moment and shear 
diagrams. 


744 ANALYSIS OF STRESSES. 


THE WARREN GIRDER. 


1332. The form of truss shown in Fig. 288 is known 
asa Warren girder. Constructed as a riveted girder, it 
is a very excellent truss for spans of moderate length. The 
distinguishing feature of this truss is that all web members 
are inclined at a uniform angle and no counter members 
are used, the counter stresses being reversed stresses in the 
main web members near the center. 







19 | 
al 
D 
3 ERS 
: : / a \ 
\ / \ / 
\ / \ v4 \ 


\ 
re i, / < 
oe MV 

ae Ria ees] 





8 





FIG, 288. 

Although not giving the best possible proportions for a 
truss of this type, for the sake of comparison, the same data 
will again be assumed for the truss of Fig. 288 that were 
assumed for the trusses of the preceding articles, namely: 
length of span, 90 ft.; panel length; 18:ft.; cheight ontruse. 
18 ft.; clear width of roadway, 18 ft.; live load, 1,800 Ib., 
and dead load, 770 lb. per lineal foot. As it isa through 
bridge, the joints of the lower chord carry the load; the 


ANALYSIS OF STRESSES. 745 


joints of the upper chord are situated midway, horizontally, 
between the joints of the lower chord. 

The stress diagrams are constructed according to the 
general principles used and explained in preceding articles. 
The student may also refer to Art. 1148, where a Warren 
girder was given as an example. 


1333. The assumption that one-third the dead load is 
carried at the upper chord joints is for through bridges ap- 
proximately correct. If, in the construction of the stress 
diagram, it be assumed that each entire panel of dead load 
is carried at a lower chord joint, then the one-third of each 
panel load belonging to the upper chord is carried in equal 
parts by the two adjacent upper chord joints. Therefore, 
the amount of error in this assumption relating to each of 
the two web members which meet at each lower chord joint 
is $ X¥ 4=4 panel load. As the stress in each web member 
bears the same relation to the corresponding vertical shear 
that the length of the member bears to the vertical height 
of the truss, the stress in each web member could be readily 
corrected in much the same manner as explained for the 
vertical members in a Pratt truss. The error of the assump- 
tion also slightly affects the chord stresses, however, and 
these could not be so readily corrected. But the error is 
very small, and is usually entirely neglected. 


1334. The correct dead load stresses may be obtained 
by constructing a stress diagram for one-half the truss, as 
shown in Fig. 288. This stress diagram is drawn for those 
stresses which relate to the left reaction, the right reaction, 
together with all loads and stresses relating to it, being en- 
tirely neglected. Only one-half of the one-third panel dead 
load at Y belongs to this stress diagram, as only that por- 
tion of this load is supported by the left reaction. This 
diagram will be readily understood without further 
explanation. 

In determining the maximum live load web stresses due 
to the left reaction, a maximum compression will be obtained 
for Dc anda maximum tension for Yc’. It is evident that 


746 ANALYSIS. OF STRESSES. 


under corresponding conditions the right reaction will pro-- 
duce .cxactly the reverseof this, i) ¢, @tensionvin. 27 eanG 
compression in J) c’. Therefore, both maximum stresses 
must be written for each of these members which are thus 
found to undergo reversals of stress under varying conditions 
of load. 


EXAMPLES FOR PRACTICE. 

1. Construct the stress diagram for the dead load stresses in the 
members in the left half of the truss shown in Fig. 288, using the data 
given above and assuming the entire dead load to be concentrated at 
the joints of the lower chord. 

Ans. For a £& + 15,490 Ib. For ¢c c’' — 20,790 Ib. 
For B C+ 18,860 Ib. For 2 6— 15,500 1b. 
For C D + 20,790 Ib. For 6 C+ 17,750 Ib. 
For a &6— 6,980 lb. For). Ge c= Fiat. 
For 6 c— 17,8380 Ib. For c D— 0,000 Ib. 

2. Compute the live load stresses in the chords and end posts from 
the corresponding dead load stresses. 

Ans. For a B + 86,220 Ib. 

For B C+ 32,400 lb. For 4 c — 40,500 Ib. 

For C D + 48,600 Ib. For cc’ — 48,600 lb. 

3. Construct the stress diagrams obtaining the maximum live-load 


For a 6 — 16,200 lb. 


web stresses, Be Mes ( + 10,870 Ib. 
Ans. For B&B 6 — 36,220 Ib. For ¢ D) — 10,870 Ib. 

For 6 C + 21,780 lb. nines 10,870 lb. 

For C ¢— 21,730 lb. / + 10,870 Ib. 


4. Construct a stress diagram similar to that of Fig. 288, obtaining 
the correct dead load stresses, assuming two-thirds the dead load to be 
carried at the joints of the lower chord, and one-third to be concen- 
trated at the joints of the upper chord. 


Ans. For a & + 15,500. Ib. 
For & C + 13,280 |b. 
For C D + 20,210 lb. 
For a &— 6,930 lb. 
For 6 ¢c— 17,880 lb. 


For c c' — 20,790 Ib. 
For 2 6 — 14,200 lb. 
For 6 C+ 9,040 lb. 
For C c— 6,460 lb. 
For ¢ D+ 1,290 lb. 


Nore.—Compare the results obtained in the solution of Example 4 
with those obtained in the solution of Example 1. 


GENERAL REMARKS. 
1335. In order to obtain reliable and accurate results 
in the graphical analysis of stresses, it 1s necessary that the 


diagram of the truss should be accurately drawn to as large 
a scale as convenient, and that the lines of the stress 


ANALYSIS=OR STRESSES. 747 


diagram should be drawn truly parallel to the corresponding 
members of the truss. Decimal scales should be used for 
stress diagrams; they should be large enough to be easily 
read to the nearest hundred pounds, except in cases where 
the use of so large a scale causes the stress diagram to be 
inconveniently large. Scales of 10, 20, 30, 40, 50, and 60 
_ parts to the inch are the scales commonly used. 

The best scales for graphical work are the ordinary paper 
(pasteboard) scales, which can be obtained 18 inches long; 
these scales also possess the advantage of being cheap. 
Besides the necessary scales, a complete outfit for graphical 
work consists of an ordinary drawing board, a T square, a 
pair of rather large 45° and 60° triangles, a rolling parallel 
rule, a hard pencil, a rubber, and a fine flat file to sharpen 
pencil. The parallel rule, though very convenient, is not 
indispensable. ‘The paper commonly used is the ordinary 
cheap detail paper. | 

It is an absolute waste of time to attempt to obtain the 
stresses in a bridge or similar structure more accurately than 
to the nearest hundred pounds. 

The student should guard against acquiring the habit of 
attempting to be unnecessarily exact. In this work, accu- 
racy, using the term in a large sense, is absolutely indis- 
pensable, but painful and unnecessary exactness should be 
avoided. Results containing no error greater than one per 
cent. will be considered correct. 

After the student becomes thoroughly familiar with the 
methods of determining stresses which have been explained 
in the preceding pages, he will be able to shorten the process 
considerably in nearly every case. 


T. I1,—9 





AE MIENY.SIS OF, STRESSES. 


(CONTINUED.) 


TRUSSES WITH INCLINED CHORDS. 


1336. All the stress diagrams in the preceding articles 
refer to trusses having horizontal chords. But such trusses 
do not afford the greatest degree of economy for long spans. 

An inclination of 45 degrees, or midway between horizon- 
tal and vertical, is the most economical for the inclined web 
members of a truss carrying vertical loads. While this 
statement applies to all the inclined web members, it, of 
course, applies to a greater degree to those members which 
bear greatest stress. Considerations of economy also re- 
quire the height of a truss at the center to bear a certain 
ratio to the length of span; this ratio varies with different 
conditions, but is usually between one-fifth and one-eighth. 
In trusses of considerable length of span this center height 
becomes so great that the diagonal members can not be 
given economical inclinations without making the panels 
longer than is permissible for wood stringers or desirable for 
the lateral systems. In such cases, therefore, special ex- 
pedients are resorted to in order to obtain, as nearly as pos- 
sible, economical inclinations for the diagonal members, 
especially for those near the ends of the truss, in which the 
stresses are very great. 


1337. In bridges of long span, some degree of economy 
of material may be obtained by properly inclining one of the 
chords. A somewhat greater economy is usually obtained 
by ‘‘curving” the chord, 1. e., by making the inclination of 
the chord between joints near the ends of the truss greater 
than between those near the middle, giving an outline for 
the chord to some extent approximating a curve. The 


For notice of copyright, see page immediately following the title page. 


750 ANALYSIS OF STRESSES. 


chord remains straight between joints. When in different 
portions of the chord the degree of inclination is thus varied, 
it is called a curved chord. When the degree of inclina- 
tion of the chord is constant from the center to either end, 
it is called an inclined chord. Curved chords give not 
only better economy of material, but also a more graceful 
outline to the truss than can be obtained by chords having 
the same inclination throughout. In through bridges it is 
almost invariably the upper chord that is inclined or curved, 
although the end panels of the lower chord are sometimes 
inclined. Ina curved or inclined chord the middle portion 
is usually horizontal; if the truss has an odd number of 
panels, the chord is always horizontal in the center panel. 

The method of constructing the stress diagram for a bridge 
having curved or inclined chords is substantially the same 
as for a bridge having parallel chords, though the form of 
the diagram is somewhat different. An example of a 
through bridge having a curved upper chord will now be 
given. 

Notre.—All stress diagrams noticed in the following pages refer 
to through bridges, which are the bridges most commonly met with. 
When the principles are thoroughly understood with reference to 


through bridges, no difficulty will be experienced in applying them 
to deck bridges. 


CURVED CHORDS. 


1338. In Fig. 289 is represented a truss of 8 equal 
panels, having a span of 140 feet. The general design of 
the truss involves the principle of the Pratt truss; that is, 
in the web system the vertical members are compression 
members, and the diagonal members are tensionmembers. It 
differs from the ordinary Pratt trussinthat the vertical mem- 
bers are of different lengths, thus varying the height of the 
truss, as shown in the figure. The clear width of the road- 
way supported by the two trusses is 16 feet. The live load 
is assumed as 100 pounds per square foot of roadway. 


1339. The Dead Load Stresses.—By formula 90, 
Art. 1298, the dead load per lineal foot, exclusive of the 


ANALYSIS OF STRESSES.- 751 


(16 —6)x 140 , 140° 
8 T 300 — 
420 lb. Assuming the floor to be white oak, from Table 
29, Art. 1299, the weight per lineal foot of floor for 
panel lengths of 18 feet is found to be 309.6 + 2 x 45.6 = 
400.8 Ib. 
_ The total dead load per lineal foot of structure is 420 + 
400.8 = 820.8 Ib., say 820 lb. As the length of each panel 


floor, is found to be 100+ 5 x 16+ 














es 820. ii 
is se =—wiitepettes-toespane)| dead load is u ee ieloe 
lb., or say 7,200 lb. For this load, by formula 89, Art. 
20 — 
Mee ae epee 5,200 Th 


In Fig. 289 is also shown a complete stress diagram for 
the dead load. By the aid of the notation it will be easily 
understood. The character of each stress will be readily 
distinguished. It will be noticed that the stresses in the 
web members are small, especially the stresses in the verti- 
cal posts. This is due to the fact that in each panel where 
the chord is inclined, the vertical component of the chord 
Stress takes up the greater portion of the shear; thus the 
vertical component of 1-172, the stress in / C, is nearly equal 
to 1-4, or the shear in the panel c d, which is carried by the 
members C DandC d to the point C, and 12-13, the amount 
of shear in this panel remaining to be carried by the post Cc, 
is very small. It is especially noticeable that the vertical 
component of 7-74, the stress in C J, is greater than 7-5, or 
the shear in the panel d ¢; and, therefore, 14-15, the stress 
in Dd, is tension instead of compression. It is evident that 
the stress in DY d will also be tension when the truss is fa//y 
loaded with the live load, as the conditions are then the 
same as are assumed for:the dead load. 

From the upper half of the stress diagram the following 
dead load stresses are obtained for the members in the left 
half of the truss: 

Stress.in @ O=— 2-10 = — 24,500 Ib. 
Sireccu age G = fen [ewe 4 OU) LD, 
Stressun @ (2 6-15.17 34.360 41b. 


W52 ANALYSIS OF STRESSES. 


Stress ind e= 5-15 = — 39,380 lb. 
Stressina B= /-10 = - 35,150 Ib. 
Stress in B C= 1-12 = + 35,250 lb. 






; 

ok 2 In ay Sars RA gn aT PY LS LTT) 

Lot ee 
ae CA caer Cc C0 es Cae aa Cees Ce es CO 
ee ap 

2 10 

3 11 Seale 1=145001bs. 

, 13 








: 19 
ey, 
‘ 20 
8 22 
- 23 
FIG. 289. 


Stress in C D= 1-14 =-+ 39,6380 Ib. 
Stress in DE = 1-16 = + 42,000 lb. 
Stress 1n. BO 10-11 = a 200 Ip, 


ANALYSIS OF STRESSES. 753 


Stress in B ¢ = 11-12 = — 14,150 Ib. 
Stress Ceo ieee — 7 2, 000 Jb: 
Stress itt Ca = 15-14 =" 8, 050; Ib: 
Stress it ae 1-1 900 Ib. 
Stress in D e= 15-16 = — 4,450 Ib. 
SiLrese ine = 10517 = 0,000 Ib. 


The above stresses for the vertical members are each to 
be corrected by adding algebraically one-third the panel 
load considered as a compressive stress, according to the 
rule given in Art. 1300. In the present case, the correc- 
tion to be added is ae 2, 4000lb. -peretore.. the cor- 


rected stresses in the vertical members are as follows: 


Stress in B 6 = — 7,200 + 2,400 = — 4,800 lb. 
Stress in Cc = + 2,950 -+ 2,400 = + 5,350 Ib. 
Stress in Dd= — 900+ 2,400 = + 1,500 lb. 
Ditess ie 000 + 2,400 = + 2,400 lb. 


1340. The Live Load Stresses.—<As_ previously 
stated, the live load assumed for the trusses is a uniform 
load of 100 pounds per square foot of roadway. The live load 
Demelitteal toot Ic mtneretore, 100. x 16 1.600. lb... and the 
1,600 X 17.5 

2 
stresses in the chords and end posts may be obtained by 
constructing a stress diagram in every respect similar 
to that explained for the dead load stresses, but they will 
be most easily obtained by observing that, since the con- 
dition of loading for the maximum live load chord stresses 
is the same as for the dead load stresses, the only difference 
being in the amount of the respective panel loads, ¢he stress 
in the two cases must be proportional to the corresponding 
loads (either per panel or per lineal foot). -Let S, be the 
dead load stress in a member, and JY the dead load per 
lineal foot (for which may be substituted the panel load); 
S, the live load stress in the same member, when the whole 
truss is loaded, and Z the live load per lineal foot (for 
which the panel load may be substituted). Then, S,;: Sj:: 





live panel load is a 14000 Ih.” Thestive load 


754 ANALYSIS OF (STRESS Ew. 


: th : 
VERGO Nees y aki bey Sees dese 7? that is, the maximum live load 
chord stresses are found by multiplying the corresponding 
dead load stresses by the ratio of the live load to the dead 
load. 

In the example, the panel live load is 14,000 lb., and the 

Ley AE O00 a 
aR Tier a kk 

Notre.—It may not be out of place to state here that the calculating 
instrument commonly known as a slide rule, though not a necessity, 


will be found very convenient in the analyses of stresses and various 
other computations relating to bridge design. 


panel dead load is 7,200 lb. Therefore 


Applying the preceding rule to our example, we get: 


stress in @ 5 = + 35,150.x = = -+ 68,350 Ib. 
stress in BC =-} 35,250 x “= -'638,/5001b: 
Stress int = 30.660 eee Oe 


stress in D2 = 49-000 x 9 Sl e00b: 





Stress ina b = — 24,500 x ‘‘ = — 47,600 lb. 
Stress in 0 ¢c = — 24,500 x “* = — 47,600 Ib. 
Stress inc ad = — 34,360 x ‘‘ = — 66,800 lb. 
Stress in @ e¢ = — 39,380 x ‘‘ = — %6,600 lb. 
Stress in. D).d = = 900 Se ee Ur 


It is evident that the live load stress in the hip vertical 
Lb is tension equal to the panel load at 6 supported by it, 
or — 14,000 Ib. 


1341. The maximum live load stresses in the members 
of the web system remain to be found. As these maximum 
stresses obtain for the different members under varying 
conditions of load, the operations for finding them, as ex- 
plained in Art. 1295, involve the construction of several 
stress diagrams, one for each condition of load. A method 
of obtaining the maximum live load web stresses by means 
of a single figure, in which the necessary portions of the 
several ‘stress diagrams are combined, together with a 
special method of shortening the operations, will now be 
explained. 


ANALYSIS OF STRESSES. 755 


In Fig. 290 is a diagram of the truss in which are shown 
those web members only which transfer their load to the 
left reaction. It willalways be found expedient to designate 
the external forces and, so far as possible, the members of 
the truss by numerals corresponding to those that were 
used for the same purposes when obtaining the dead load 
stresses. Below the diagram.of the truss are the com- 
bined stress diagrams for the varying live load, which are 
constructed as follows: 

Upon the load line are laid off in order the /ef/¢ reaction 
from a full live load and that portion of each separate 
panel load that is supported by it; taking the external forces 
in order, passing around the truss to the left, but omitting 
all portions of the live load relating to the rzgh¢ reaction, 
as explained in Arts. 1327 to 1329. The portion of the 
panel load (14,000 1b.) at each joint, which is supported by 
the left reaction, is as follows: 


Load at 4 or 2-8= 1X 14,000 = 12,250 Ib. 
[ead AG. Oras ee DUEL). 500 1b: 
Load at d or 4- Bb sae OU 1; 
Load.at 2-01-66 = 4x.14.000= 7,000 Ib. 
Gateat ge fea a4 OOO = 622.50: Lb. 
[eaten (63-2. 14 000 33,500: Ib- 
LEodadiat @ ors-f== 4.x 14,000 =» 12750 Ib. 


Total reaction A, from full load = 49,000 Ib. 


l= cleo cots ol aolen ale 


Upon the load line, 7-2 is laid off upwards equal to X&,, 
then 2-3, 3-4, 4-5, etc., each equal to that portion of each 
respective panel load supported by the left reaction, are 
laid off in order downwards to the starting point. Also, 
from 7 are laid off upwards the amounts J,-6, and 6,-7,, 
equal, respectively, to the half panel load of dead load at e 
(5-6) and to the panel load of dead load at @d' (6-7) which 
are supported by the vzg#¢ reaction. This is conveniently 
obtained from the load line in the stress diagram for the 
dead load, Fig. 289. In Fig. 290 the dead load supported by 
the right reaction is laid off wpwards along the load line in 
precisely the same manner that it extends downwards upon 


756 ANALYSIS OF STRESSES. 


the load-line in) Fig/289, except that ites aids ol stomoue 
scale used for the live load, and that only such portion of the 
dead load need be thus laid off as will bring some numeral 
for the dead load, as 7,, above the corresponding numeral 
for the live load, as 7. It will be expedient to draw through 
1 the lines 1-12,, 1-14,, and 1-16,, of indefinite length, and 


Oo? 





12 


14, 


16, 





Fic. 290. 


parallel, respectively, to the upper chord members B C, C D, 
and D £. 

On the load line, 7-2 represents the reaction from a full 
load, which condition gives the maximum stresses in the 
chords and end post; /-2-10-1 is the force polygon for joint 
a, giving the maximum stresses in a 4 andaJv. As these 
stresses have been obtained above from the dead load 


ANALYSIS OF STRESSES. 157 


stresses, this force polygon serves merely to check the 
accuracy of the work. 

The stress in 4c obtains its maximum value with joint J 
unloaded, all other joints remaining loaded. Since in this 
condition no external force is applied at joint J, the external 
force &, applied at ais designated by 1-3; also, as no internal 
_ force is acting in B 6, the entire space between a £ and B c 
is designated by the one numeral 7/17. 


(2) When two or more original spaces are combined as one 
space, on account of the intervening force or forces having 
been removed, consider the entire space thus combined to be 
designated by the numeral of the original space furthest at 
the right. 


On the load line, 7-3 is the reaction from this load and 
1-3-11-1 is the force polygon for joint a; for joint B 1-11-12-1 
is the force polygon, giving the maximum stress in & ec. 

For the maximum stresses in C d@ and C ¢, the joints 0 
and c must carry no load, and all other joints must be loaded. 
For this load, 7-4 represents the reaction and 1-4-11,-1 is the 
force polygon for joint a. For joint 4, 1-11,-12,-1 is the 
force polygon; 12,-11,-4-13,-12, is the polygon for joint ¢; 
and 1-12,-13,-14,-1 is the polygon for joint C, in which 
Peed 13-22 represent the maximum: stresses in C.¢ 
and C d, respectively. The operation of finding the maxi- 
mum stresses in these members may be somewhat shortened 
by a special method based upon the following principle: 

(6) Tf, with no loads at b and c, all portions of the truss 
at the left of the member C ad were considered to be removed 
and replaced by the member a C, represented by a dotted line, 
and the chord ad, the stress in C ad and in cach member of 
the truss at the right of C ad will remain unchanged. 


This is a general principle, and may be stated as follows: 


(c) Lf, while the entire loaded portion of any truss re- 
mains unchanged, all that portion of the truss, situated 
between the reaction and the nearest load, be considered 
removed and replaced by two members which extend, re- 
spectively, from the reaction airectly to the nearest upper and 


758 “ANALYSIS OF STRESSES. 


lower chord joints in the unchanged portion of the truss, then 
the stress in cach member inthe latter portion will remain the 
same as though the entire truss were unchanged. 

In the diagram of the truss, as thus modified, the entire 
space at the left of C d will be represented by the numeral 
18; that is, by the numeral which originally represented the 
first space at the left of that member. Onthe load line, 7-4 
represents the reaction, and /-4-13.-1 is the force polygon 
for joint a, the lines 4-78, and 13,-1 being drawn parallel to 
the new members a d@ and a C, respectively.. The force 
polygon 1-13,-14,-1 may now be drawn for joint C, giving 
the line /3,-14, to represent. the maximum stressin C d. 
But as, in drawing this polygon, C ¢ was assumed to have 
been removed, the polygon does not give the stress for this 
member. ‘To obtain this stress, consider the members of the 
truss at the left of Ca to be restored tomtheir one 
nal positions; then, by passing in the offoszte direction 
around the joint C, the polygon 1-14,-13,-12,-1 may now be 
drawn, in which /2,-73, represents the maximum stress 
ine 

For the maximum stress in D ¢ and D d, the joints J, «, 
and @ must carry no load, and all other joints, i. e., all joints 
to the right of the panel de, must be loaded. All members 
of the truss at the left of )) e are considered to be removed, 
and the members a ) and @e substituted; the entire space 
at the left of D eis represented by 15, the numeral furthest 
to the right in this space. 

The reaction from this load is represented on the load line 
by 1-5. For joint a of the truss as modified, 1-5-15,-1 is the 
force polygon; the force polygon for joint D is 1-15,-16,-1, 
giving 15,-16,as the maximum stress in De. The members 
of the truss at the left of De are now considered to be re- 
stored to their original positions, and in this condition the 
reversed polygon for joint D is 1-16,-15j-14,-1, in which 
14,-15, represents the maximum stress in D @ 

For the maximum stresses in / d@' and £ g, all joints to the 
left of the panel ¢ @’ must be unloaded, and all joints at the 
right of it must be loaded. To obtain the stress produced 


ANALYSIS OF STRESSES. 759 


in & d' by this load, the members a / anda d' are considered 
to be substituted for all portions of the truss at the left of 
fd’, The entire space at the left of £ d'is now repre- 
sented by the numeral 17, and, since no external forces are 
applied between a and @’, the left reaction is represented by 
¥-G4 Onitne load line J-6 represents the reaction for this 
- load; for the truss as modified, /-6-17,-1 is the force polygon 
for joint a. Considering the members of the truss at the 
left of / ad’ to be restored to their original positions, the 
force polygon for joint 4, found by taking the forces in the 
reverse order around the point, is /-18,-17,-16,-1. 

The lines 16,-17, and 17,-18, would represent the maximum 
live load stresses in & e and £ a’, respectively, were it not 
that the panel ¢ @’ is situated at the rzght¢ of the center of 
the truss, and, therefore, the zegative dead load shear in this 
panel counteracts a portion of what would otherwise be the 
stresses in these members produced by the positive live load 
shear. One-half the panel of dead load at e is supported by 
the right reaction; in traveling towards the reaction this 
half-panel load produces negative shear in the paneled’. 
In the stress diagram this half panel of negative shear is 
represented by 4,-6,. Therefore, through 6, draw the hori- 
zontal line 6,-18,; then, 16,-17, and 17,-18,, will represent the 
resultant maximum live load stresses in & e and & ad’, 
respectively. 

For the maximum live load stress in J’ c’, the joint @’, 
as well as all joints to the left of it, is unloaded, while all 
joints to the right of it remain loaded. For this load, the 
left reaction is represented on the load line by 1-7, which 
also represents the positive shear in the panel @’ c’, as well 
as in all panels at the left of it. But the negative shear in 
the panel d'c’ is equal to one-half the panel load of dead 
load at e plus the panel load at @’, represented on the load 
line by 5,-6, and 6,-7,, respectively, the total amount being 
represented by 4,-7,. As 4,-7, is greater than 1-7, no posi- 
tive shear can occur in this panel, and hence no stress can 
besomtaneurtorsaecounter J) a. In the figure the dead 
load numeral 7, is situated at a point upon the load line 


760 -ANALYSIS OF STRESSES. 


above the live load numeral 7; therefore, no positive live 
load shear is found in the panel 7, or @’c’. But the dead 
load numeral 6, is below the live load numeral 6, and _ post- 
tive live load shear’is found to exist in the panel 6, or 
as Se 

The above method should be employed for determining 
the counter stresses in all panels in which both chords are 
horizontal, as in the paneled’. It is not to be relied upon 
when this is not the case. 

By measuring the lines of the stress diagram to the scale 
used in laying off the load line, the following maximum 
stresses are obtained: 


otress:in'@ 6 ==) 2-J0 (= — 47,640 Ip, 
Stressina Bb = 1-10 = -+ 68,350 lb. 
Stress in Bc = 11-12 — 32,620 lb. 
tress: in Go) = 12 316 = 0 Uae 


Stress in C7 ="13,-14,.— — 25,160 Ib. 
Stress ‘in Da. ==-74,-16,, = 4- 13,1380 Ib. 
Stress in De = 15,-16, = — 21,660 lb. 
Stress in A ¢ = 16,-17,= + 6,900 Ib. 
Stress in £ d' = 17,-18,, = — 8,540 Ib. 


1342. The Lateral Stresses.—The dimensions of 
the chords are necessarily greater in bridges of long span 
than in bridges of short span. For short spans, the width 
of achord may, for the purpose of calculation, be taken equal 
tol foot. stor spans longer than 120 feet, consider the width 
of the chord in inches to be py the length of the span tn feet. 
If Zis the length of the span in feet, then, width of chord = 
ie nen es' = — feet. 

The width, center to center of chords, equals the clear width 
of roadway plus the width of one chord. 

Let C = width center to center of chords, 6= clear width 
of roadway, /= length of span. Then, 


C=b+ 75. (101.) 


ANALYSIS OF STRESSES. 761 


1343. For lateral systems of bridges having curved or 
inclined chords, the panel concentrations of wind load are 
found in the same manner as for horizontal chords, since the 
amount of wind force per lineal foot of structure is the load 
usually (though not always) specified. But in drawing the 
diagram of the truss of the lateral system extending along 
_the curved or inclined chord, from which to construct the 
stress diagram, the length of each respective panel should be 
made equal to the correct length of the panel measured along 
the inclined chord. 

Thus, in the truss shown in Figs. 289 and 290 the panel 
length, measured horizontally, is 17.5 feet; but for the upper 
lateral system the lengths of the panels 5 €, C D, and DE 
are, respectively, 17.95, 17.61 and 17.5 feet. For this purpose 
it is sufficiently accurate to measure their distances on the 
diayram of the truss. 


1344. Ina system of lateral bracing of the Pratt truss 
type the live load stress for the lateral strut at the center, as 
given by the stress diagram, will sometimes be less than a 
panel load; in such cases the live load stress should be taken 
equal to one panel live load, as it is evident that with the 
adjacent panels loaded, the stress in this strut will equal 
thatamount. This statement apples also to the vertical 
post at the center of a Pratt truss deck bridge, in which ¢he 
maximum live load stress 1s never less than a panel load. 


EXAMPLES FOR PRACTICE. 

1. Using the data given in this article, construct the stress diagram 
shown in Fig. 289, obtaining to the nearest hundred pounds the dead 
load stresses which have been given for the same. 

2. Construct the stress diagram, obtaining the live load stresses in 
the chords and end posts. 

3. Check the results obtained in the solution of the preceding 
example by multiplying the corresponding dead load stresses by the 


Tatio L 
W 


4. Construct the combined diagrams, obtaining to the nearest 
hundred pounds the maximum live load web stresses given above. 


762 ANALYSIS. OF STRESSES. 


FORMULAS FOR CHORD STRESSES. 


1345. The stress in any horizontal portion of either 
chord in a truss of the Pratt or Howetype, when fully loaded 
with a uniform load, may be obtained or verified by applying 
the following formula: 


/ 
| (= Pe — ae x mm, (eke) 
in which P is the panel load, fis the panel length, % is the 
height of the truss at a vertical member, 7 is the number of 
panels at the left, and zz’ the number of panels at the right 
of the vertical member, and C,, is the stress in that portion 
of either chord situated between the same two diagonal 
members between which is situated the vertical member at 
which / is taken. The formula, of course, is to be applied 
to one-half of the truss only ; the stresses in the other half 
are the same, respectively, as those found for the first half. 
This is a very convenient formula, andits use is illustrated 
in the following 
EXAMPLE.—Find the dead and live load chord stresses for a Pratt 
truss of 8 panels, in which panel length = 20 ft.; height of truss = 24 
ft.; panel live load = 11,200 lb., and panel dead load = 7,400 1b. Let 
the portions of the lower chord be 26,\0c,¢d, de, ea ,d C.2.0, 008 
SOLUTION.—For dead load, we have, | 
Pp _ 7,400 x 20 
2 A Ee ot 
The values of #z7' for the different panels are: 
Fors, 4197 =o bes 
Nore 2d, wim = OX? S13 lee: 
' Ford 2) mw 0x 8 Sb Hee. 





= 3,083, nearly. 


Then, we have, 


% < 3,083 = — 21,581 lb. = stress in @c. 

Add 53,088 = 15,415 
— 36,996 lb. = stress in cd. 

Add 3 xX 3,083 = 9,249 


= 46,245 lb. = stress in de. 


It will be noticed that, since, for instance, 12='%7-+5, in order to 
multiply 8,083 by 12, we have to multiply by 5 only, and add the 
product to 7 x 3,083, already found. ‘The same with other products. 


ANALYSIS OF STRESSES. 163 


For live load, 
Pp 135200 20 
2h ~) 2x 24 
Then, as before, 


7 x 4,667 = — 32,669 lb. =stress in ad and dc. 
Add 5X 4,667 = © 23:335 
— 56,004 lb. = stress in cd. 
Add 3% 4,667 = 14,001 
— 70,005 lb. = stress in de. 


Stresses in other half are the same. For upper chord, ¢he stress zn 
every portion of it ts the same in amount as, but of opposite kind 
to, the stress in the portion of the lower chord included between the 
same main diagonals. ‘Thus, stress in AC (first portion of upper 
chord) = mznus stress in cd = + 56,004. 


1346. If the portion of either chord to which the for- 
mula is applied is zzc/ined, then C,, will represent the “orzzon- 
tal component of the chord stress, and the latter may be 
obtained by applying the following formula: 

Ci k 

C= ghee 

in which £ is the panel length measured along the inclined 

chord (i. e., the length of the inclined member in question), 

(is tue stress in the sdme,,.and /# is the panel lenoth,-as 
before. 

Chord stresses may readily be obtained by applying the 
preceding formulas 102 and 103. But the dead load chord 
stresses and web stresses are both obtained by constructing 
the stress diagram; and if the live load chord stresses are 
obtained by multiplying the corresponding dead load stresses 





= 4,667, nearly. 











(103-.) 


Dyecheeratio @ the entire operation may be checked by 


applying the formulas to verify the results. 


EXAMPLE.—Verify the dead load stress obtained graphically for the 
. lower chord member ¢@e of the truss shown in Fig. 289, using the data 
given therefor in Art. 1338. 

SoLuTION.—In this case, P = 7,200, 2 =—17.5, and 4=— 24; as Dd is 
the vertical member between the diagonals Cd and /)e, between which 
de is situated, #—3 and m' —5. 


7,200 x 17.5x38x5 
(Dherétores ©), = Pea esas 39,375 lb, 


I. II,—10 


764 ANALYSIS OF STRESSES. 


EXAMPLE.—Verify the dead load stress obtained graphically for the 
upper chord member C PD of the same truss. 

SoLution.—As C PD and de lie between the same two diagonals, the 
amount of stress found above for @ ¢ is also the horizontal component 
of the stress in C.D. The length of CD =//17.8 + 2=17.614 ft.= &, 


39,375 < 17,614 
and # = 17.5, as before. Therefore, C= ———qWr5 = 39,681 Ib. 





EXAMPLES FOR PRACTICE. 
1. Verify all the dead load chord stresses for the truss shown in 
Fig. 289, Art. 1338, using the data given therefor in that article. 


2. Verify all the live load chord stresses for the same. 


INCLINED CHORDS. 
1347. Aspreviously stated, trusses with inclined chords 
are usually less economical, and have not as graceful outlines 





9 123 


FIG. 291. 


ANALYSIS OF STRESSES. 765 


as trusses with curved chords. Nevertheless, bridge trusses 
having inclined chords are not uncommon. 

When the inclination of the chord is considerable, the 
counter stresses, and even the dead load web stresses near 
the center, usually become quite irregular, and sometimes 
rather complicated. In trusses of the Pratt type, however, 
‘they do not become ambiguous. An example illustrating 
this feature will now be given. 


1348. The length of span, number of panels, and the 
amount of both live and dead loads will be assumed to be 
the same as in the example for curved chords, explained in 
Art. 1338. 

The general form of the truss will also be the same, except 
that while the heights of the truss at the hips and at the 
center will be, respectively, 18 and 24 feet, as in the former 
example, the upper chord will be straight between those 
points, as represented in Fig. 291. 

The Dead Load Stresses.—The stress diagram for 
the dead load, assuming the panel loads to be concentrated 
at the joints of the lower chord, is also shown in Fig. 291. 
Some peculiarities in this diagram will be noticed. The 
force polygons for joints a, 6, B, c,and C are each con- 
structed in the usual manner, and will be readily understood. 
For joint d, the lines 74-73 and 13-4, parallel, respectively, to 
the members @ C and dc, are retraced, the pencil is passed 
down the load line the amount 4-5, equal to the panel load 
at d, and from 4 it must be returned to the starting point 
14 by lines drawn parallel, respectively, to the two remain- 
ing forces which act upon this joint, of which one is stress 
in the chord member d e¢, and the other must be stress in 
either the compression member /) d or in the tension mem- 
berd #. For, by drawing through the point 5 a line of 
indefinite length parallel to d@ e, as the line 5-16, it can be 
readily discerned that the polygon could be closed by a single 
line drawn from some point on the line 5-/6 parallel to either 
of these members, showing that it is necessary for but one 
of them to act; it can also be seen that, as the line 5-6 lies 


766 ANALYSIS OF STRESSES. 


below the starting point 14, the general direction of the 
closing line must be upwards, showing that the correspond- 
ing force or stress acts in an upward direction upon joint d. 
It isevident that a stress in either Dd or d #, acting in an 
upward direction upon this joint, must necessarily be tension, 
and must act in a correspondingly downward direction upon 
the joint at the opposite end of the member. It is evident 
that this downward action can not be resisted at Y without 
causing bending moment in the upper chord between C and 
f, which is not permissible; it is also evident that this 
downward force, if transferred by the member d £ to joint 
f:, can be resisted at that point by the ‘vertical component 
of the stress in the upper chord) =Asmit4s thenstound thar 
the forces acting upon joint @ can be held in equilibrium 
only through tensile stress acting in the diagonal d £, there- 
fore this member is known to act in this condition of load 
(i. e., when the truss is loaded with the dead load only); 
consequently, a line must be drawn parallel to it in the 
polygon for joint @. The line 76-15, in this polygon, can be 
so drawn that the point 75 will coincide with the starting 
point 74; the line 75-14, which represents the stress in D d, 
has, therefore, no length (i. e., there is no line 15-14), and 
the stress in dis zero. As but one diagonal in a panel 
can act in the same condition of load, the diagonal D e does 
not act when the truss is loaded with the dead load only, 
as will also be determined by the force polygon for 
joint e. Considering the forces which act upon this joint, 
the line 16-5 is retraced, the pencil is passed downwards 
upon the load lne the amount 4-6, equal to the panel 
load at e, and it is found that from 6 the pencil can be 
returned to the starting point 16 by the lines 6-17 and 
17-16, drawn parallel, respectively, to the members e¢ d' 
and @ £&, giving no ‘stress for the) members “Deeeand 
Cale. 

In this polygon the line 6-17, representing the stress in 
ed', is found to equal 16-5, which represents the stress in 
ad ¢e, as should be the case at the center of a symmetrical 
truss having an even number of panels. Alsothe line 7-16, 


ANALYSIS OF STRESSES. 767 


which represents the stress in & ge, is found to equal 5-6, or 
the panel load at ¢, which evidently should be the case when 
there is no stress inthe members ) eand e D’. Considering 
next the forces which act upon joint 4, the lines 1-15, 15-16, 
aiuesvo-i/eare retraced, and it 1s found: that from J7 the 
pencil can be returned to the starting point / by lines 
_ 17-18 and 18-1, drawn parallel, respectively, to & d’ and 
i D"; this gives 17-18, the stress in & d', which is equal to 
15-16, the stress in & d, and also gives 18-1, the stress in 
£ D', which is equal to 1-15, the stress in & D, as should be 
the case. 

The polygons for the joints in the right half of the truss 
are the same as for those in the left half; they will require 
no special explanation. In the diagram of the truss those 
members which do not act when the truss 1s fully loaded are 
represented by dotted lines. 

By measuring the lines of the stress diagram, the 
following stresses are obtained: 


mttess dt dao oI — 85 1b 0alb: 
stressin B C= 1-12 =- 38,040 lb. 
stressinm © J7— F-1,—- 43,230 Ib. 
Stressin DA= 1-15 = + 43,230 lb. 


otress ina b= 2-10 = — 24,500 |b. 
stressin. 2 ¢— 9-11 = — 24 500 Ib. 
Stressinc @= 4-18= — 37,800 lb. 
etress ined @= 4-16-— —.42,000 Ib. 
Stress in B b= 10-11= — %,200 lb. 
mllessin O..¢ = i-J — —— 9.080 Ib. 
mlicaeD Ge 1-13. 4--) 04.8021, 
stress in'C d= 13-14— — 7,830 Ib. 
Stress in D d= 14-15 =-+ 0,000 lb. 
stress in d A= 15-16 = — 1,620 Ib. 
stress in & e= 16-17= — 1,200 Ib. 


The above stresses for the vertical members must be 
corrected by adding to each, algebraically, one-third of a 
panel load, or 2,400 1b. Therefore, 


768 ANALYSIS OF STRESSES. 


Stress in Lb b= — 7,200 + 2,400 = — 4,800 Ib. 
Stress in C c= -++ 6,480 + 2,400 = + 8,880 lb. 
Stressin Dd=  0,000-+ 2,400 = + 2,400 lb. 
Stress in & ¢ = — 7,200 + 2,400 = — 4,800 Ib. 


1349. The Live Load Stresses.—The maximum live 
load stresses in the chords and end posts may be obtained 
either by multiplying the corresponding dead load stresses 


by the ratio i as previously explained (Art. 1340), or by 


constructing a stress diagram similar to that in Fig. 291. 
Neither method will require special explanation. For the 
same condition of load and in the same operation the stresses 
ind / and & emust be obtained. The stress thus obtained 
for & e will be the maximum live load /enszon in that mem- 
ber, while the stress thus obtained for the tension member 
d / may or may not be the maximum tensile stress in that 
member; it may or may not be exceeded by the stress due 
to a partial load. The latter stress will be found for the 
corresponding web member £ @’; the greater of the two 
stresses must be taken as the maximum live load stress for 
each member d £ and £ @’. 

The live load stresses in the chords, end posts, and in the 
two web members mentioned above, are as follows: 


30 


otréss in alb =e 357150 x hice + 68,350 Ib. 
stress in BS (Cr 38 140-6 eo 060 Ike 
Stress in CD = + 43:230 x ‘= + 34,050 Ib: 
Stress in D & = + 43,230 x ‘* = + 84,050 lb. 
Stress ina 6 = — 24,500 x ‘* = — 47,640 lb. 
Stress ind’ c= — 24,500 x ‘* = — 47,640 Ib. 
otress ing @=1== 37,800 <9 = 75, 000) IB: 
Stress ind e¢ = — 42,000 xX ‘‘ = — 81,670 Ib. 
mtress.in. ds) f= GRO ee oe 


Stress in £. ¢@ = '—" 7,200. x) = 14, 0004b: 


In applying formulas 102 and 1093 for verifying the 


ANALYSIS OF STRESSES. rash) 


chord stresses, it must be noticed that with the truss fully 
loaded the vertical member VP d is situated between the 
diagonals Cd and £ d, and, therefore, formula 102 applied 
at D d will give the horizontal component of the stress in 
Pieecnords Ge /a(Cy/ and J) ), Also, that the vertical 
member & ¢ is situated between the diagonals & d and F a’, 
and, therefore, formula 102 applied at / e will give the 
’ stress in the chord de and ea’, orda'. 


1350. For the web stresses which obtain from partial 
loads, the combined stress diagrams are shown in Fig. 292. 
The respective portions of the panel loads which are sup- 
ported by the left reaction are laid off upon the load line in 
precisely the same manner as was explained in Art. 1341 
for the load line in Fig. 290, but the dead loads are not laid 
off upwards from the bottom of the load line, as in that 
example. 

Beginning with the polygon 1-2-10-1, the force polygons 
for the several joints and for the various conditions of load- 
ing are drawn in the same manner as explained or Fig. 290, 
as far as and including the reversed polygon 1-16,-15,-14,-1 
for joint DY. For joint 4, the polygon 1-17,-18,-1 and the 
reversed polygon 1-18,-17,-16,-1 are also drawn in the same 
manner, but from the stresses thus obtained xo deduction ts 
made for the negative shear from dead load, as was done in 
the previous case. No negative dead load shear is deducted 
from the positive live load shear in the panel ed’, which 
produces stress in & @’' and & e, because, by consulting the 
stress diagram for the dead load (Fig. 291), it is found that 
the entire panel load of dead load at e, by which the nega- 
tive shear in this panel is produced, is carried by the member 
fetothe upper chord joint 4, and is there taken by the 
vertical component of the chord stress; consequently, the 
negative dead load shear «in the panel ¢ @’ does not in any 
way affect the diagonal members & @’ and e J in this 
panel. 2 

The maximum positive shear in the panel @’ c’, due to the 
live load, occurs when joints @’, c’, and 0’ are loaded, and all 


770 ANALYSIS OF STRESSES. 


joints to the left are unloaded. The left reaction from this 
condition of loading is represented on the load line by 1-7. 

This being known, the next step is to ascertain to what 
extent the negative shear in the panel d’ ¢’ affects the diag- 
onals in that panel, in order to determine whether any re- 





2 10 


3 41 Scale 1=20000 lbs. 


ee 


BiBe, 
ee 
19, 


18, 
FIG. 292. 
sultant positive shear can obtain in the panel. One-half the 
panel load of dead load at e, together with the entire panel 
load of dead load at @’, produce negative shear in this panel 
(d'c'); but, by again referring to the stress diagram for the 
dead load, it can be seen that not only the entire panel load 


ANALYSIS OF STRESSES. val 


of dead load at ¢, but also a portion of the dead load at a’, is 
carried to joint /, and there taken by the vertical component 
OmulesCHOruistresss | Nerelore, the dead joad at @ sand as 
much of the dead load at d' as is carried by the diagonal 
a@' f to the joint /, being supported wholly by the chord, 
do not affect the diagonals in the panel @’ c’. But that por- 

tion of the dead load at @' which is carried by the diagonal 
_a' C' (not shown in figure) is the only portion of the 
dead load which affects the diagonals in this panel; it may 
produce the amount of dead load negative shear resisted by 
d' C', or it may counteract a corresponding amount of posi- 
tive live load shear. This amount of negative shear which 
affects the diagonals in the panel @' c' is equal to the verti- 
cal component of the line 79-20 in the stress diagram for the 
dead load, Fig. 291. If in this stress diagram the point 79 
be projected upon the load line by the horizontal line 19-79’, 
then 7-19’ will represent the amount of negative shear in the 
Pane? ¢ carted by the-chord ./) 9G iand./9'-7 willirepre- 
sent the amount of negative shear which affects the diago- 
nalsin that panel. By laying off upwards from 7 on the load 
line of the stress diagram for the live load (Fig. 292), the 
amount 79,-7,, equal to the amount /9'-7 obtained from the 
load line of the stress diagram for the dead load, making due 
allowance for the difference of scales, if any, a comparison 
is obtained between the positive live load shear and the neg- 
ative dead load shear affecting the diagonals in the panel 
Wee bic amount 19,-7, — 5,990 lb. is found to be greater 
than the live load reaction 7-7 = 5,250 lb., and, therefore, 
no positive live load shear can obtain in the panel @' c’; or, 
in other words, as the dead load numeral 7, is situated at a 
point upon the load line above the live load numeral 7, no 
positive live load shear can obtain in the pane! under which 
the corresponding numeralis situated. Since, however, the 
point designated by 7,, is so near to the point designated by 
fore qdumother words, as 6,090 lb, 4s "so little in* excess of 
beeoU De, it willbe best to place a liehtcounter tie J’ c’ in 
this panel, although no stress is obtained for it. 

By measuring the lines of the combined diagrams thus 


002 ANALYSIS OF STRESSES. 


constructed, the following web stresses are obtained for the 
respective conditions of partial live load: 


Stress ina B= 1-10 = + 68,350 Ib. 


Stress in B ¢= 11 -12 = — 41,000 lb. 
Stress in C ¢ = 12,-18, = + 21,000 Ib. 
Stress in C d = 13,-14, = — 25,370 1b: 
Stress inj ad = 14,-15, = + 12,730 IB. 
Stress in D ¢e= 15,-16, = — 14,910 |b. 
Stress in A ¢= 16,-17, = + 7,000 Ib. 
Stress in £ ad’ = 17,-18, = — 18,900 lb. 


By comparing the stress (18,900 lb.) in & ad’ as found 
above for a partial load, with the stress (3,150 1b.) as pre- 
viously found for the corresponding web member @ £, when 
the truss was considered to be fully loaded, the former stress 
(18,900 lb.) is found to be the maximum stress for each of 
these members. 

As the dead load is always present upon the truss, the cor- 
rected dead load tension in & e (— 4,800 lb.) must be deducted 
from (added algebraically to) the live load compression 
(+ 7,000 lb.) obtained for it above, in order to obtain the 
net or resultant live load stress in that member. The cor- 
rect maximum compression obtained for & @¢ is, therefore, 
+.7,000 — 4,800 = 2,200 Ib. 


1351. In trusses with inclined chords the stresses in 
the web members near the center of the truss, developed by 
a full load, are not always of the same nature as in the ex- 
ample which has just been illustrated. For instance, if in 
the truss of that example the inclination of the upper chord 
were less, a full (live or dead) load would produce stress in 
the diagonals D e¢ande LJ’ instead of ind Hand Ed’. Or 
the inclination of the chord could be such that neither the 
dead load nor a full live load upon the truss would produce 
stress in any diagonal in the two center panels. In a truss 
with curved chords, the chord could have such inclinations 
that no web stresses would be produced by a full quiescent 
load. 


ANALYSIS OF STRESSES. 773 


A careful comparison of the stress diagrams, and of the 
stresses obtained therefrom, for these different forms of 
trusses having the same span, the same loads, and nearly the 
same form, the stress diagrams for two of which have been 
explained in detail, will be found very instructive. From 
such comparisons may be obtained practical and valuable 
ideas concerning the principles of economic design. 


EXAMPLES FOR PRACTICE. 


1. Construct the stress diagram for the truss having inclined 
chords, when carrying a full live load, obtaining the live load stresses 
in the chords and posts as previously given. 


2. Construct the combined stress diagrams for the partial live 
loads, obtaining the maximum web stresses as previously given. 


1352. The truss shown in Figs. 291 and 292 is a 
single intersection truss with inclined chords; it is 
commonly knownasa camel-back truss. The latter name 
is also applied to the form of truss shown in Figs. 289 and 
290; but this truss is more properly a single intersection 
truss with curved chords. These two forms of trusses 
are also known as the Pratt truss with inclined chords 
and the Pratt truss with curved chords, respectively. 
By the latter names these trusses are distinguished from all 
other forms of trusses, although, correctly speaking, neither 
truss has the exact form of a Pratt truss. But, by having 
vertical compression members and diagonal tension mem- 
bers extending horizontally through but one panel, both 
trusses embody the prominent features of the Pratt truss. 


THE WHIPPLE TRUSS. 


1353. As previously stated, an angle of 45 degrees with 
the horizontal chord is the most economical inclination for 
the diagonals of atruss. Ina Pratt truss, therefore, consider- 
ations of economy require the panel length to be approxi- 
mately equal to the height of the truss. As the height of 


774 ANALYSIS OF STRESSES. 


the truss increases with the length of the span (Art. 1336), 
it follows that in long spans the diagonal members of a Pratt 
truss can not be given an economical inclination without 
making the panels longer than would be desirable. In long 
(and consequently high) trusses, the diagonals may be given 
an economical inclination without requiring excessively 
long panels, by combining two systems of Pratt truss 
bracing, forming what is known as a Whipple double 
intersection, or double quadrangular truss. 

A truss of this type 1s shown in the upper portion of Fig. 
293. In this truss the panel length is equal to one-half the 


DUR aero Ge hoes 2p ae eRe 


ANSE, 
ANKE 


D’ B’ 











a b d f (b) fe d’ bv’ a’ 
FIG. 293. 


height; the diagonals have an inclination of 45 degrees. 
One system of web bracing is shown by dotted lines, and one 
system is shown by full lines. An analysis of the stresses 
may be obtained by separating the two systems. In (a), Fig. 
293, 1s shown the system of bracing which in the upper figure 
is represented by full lines, while the system represented in 
the latter figure by dotted lines is shown at (0). In Figs. 
(z) and (0), those diagonals of the respective systems which 
do not bear stress when the system to which they belong is 
fully loaded are represented by dotted lines. 


ANALYSIS OF STRESSES. ras) 


A slight ambiguity occurs in the web stresses, due to the 
fact that it is not known by which system the panel loads at 
6 and $6’are carried; but the assumption usually made, 
namely, that one-half of each load is carried by each 
System litistabe very nearly. correct,, he-error,; if any; is 
small. 


1354. The following data are assumed for the truss 
shown in Fig. 293: The length is 198 ft.; as it is divided 


: Sal, 
into 12 equal panels, the length of each panel is ss SSubo Di Lt, 


Thesheight of the truss is 33 ft. The clear width of road- 

way supported by the two trusses is 20 ft., and the live load 

for the trusses is a uniform load of 80 lb. per sq. ft. of 

roadway. The live load per lineal foot is, therefore, 

80 x 20 = 1,600 lb., and for one truss the panel live load is 

1,600 x 16.5 
2 





= 13,200 lb. 


1355. The Dead Load Stresses.—By formula 91, 
Art. 1298, the dead load per lineal foot, exclusive of the 
floor, is 80 + 100 + 248 -++ 131 = 559 Ib. 

From Table 29, Art. 1299, the weight per lineal foot of 
a yellow pine floor for a panel length of 17 feet is 274.5 + 
Ape AU ol Lueretore. the, dead load. per, lineal 
foot is 559 + 437 = 996 lb., or say 1,000 lb. For one truss 
1,000 X 16.5 

2 

Considering first the system of bracing shown in (a), Fig. 
293, and remembering that but one-half of the panel loads 
at 6 and at 6’ are borne by this system, the value of either 
reaction 1s 8,250(43 X¢+He+&etwetat wat dt X 4) 

é bee 
= De WOU OX 13 = 
laid off upon the load line, and the stress diagram is con- 
structed in substantially the same manner as previously 
explained for the dead load. The extreme upper and lower 
portions of the load line represent the half panel loads 


the panel load is, therefore, = 8,250 lb. 











24,750 lb. The full loads and reactions are 


776 ANALYSIS OF STRESSES. 


(4,125 lb.) at 6 and 0’, respectively, while each intermediate 
division represents a full panel load (8,250 Ib.), otherwise 
the construction is regular, and will require no special 
explanation. Bow’s system of notation can be used. 


1356. The live load stresses in the chords and end 
posts of this system may be obtained by constructing a 
stress diagram similar to that for the dead load; or they 
may be obtained by multiplying the corresponding dead 
Dol ae OU 
load stresses by the ratio D = 1.000 = 

For the live load web stresses, the left reaction and those 
portions of the respective panel loads which are supported 
by it are laid off upon the load line in the manner explained 
in Art. 1341. The right reaction die to live loaawie 
entirely neglected, but the portions of dead load producing 
negative Shear in the panels at the right of the center ace 
laid off upwards from the bottom of the load line, as was 
also explained in Art. 1341. For this system the left 
reaction from live load and the portions of each panel load 
supported by it are as follows: A,=13,200(44 x 4-4 18- 
3 + 45+ #%+ 4+ a Xx 4) = 6,050 + 11,000 + 8,800 + 
6,600 + 4,400 + 2,200 + 550 = 39,600 lb. The reaction is 
laid off upwards and the proper portions of the respective 
loads, as thus found, are laid off in order downwards to the 
starting point. The combined stress diagrams for the 
partial loads are constructed substantially as explained in 
Art. 1341. 

The process of obtaining the stresses for the system of 
bracing shown in (0), Fig. 293, is very similar to the above. 
The principal difference is that the system of bracing shown 
in (0), Fig. 293, has an odd number of panels, while that 
shown in (a), Fig. 293, has an even number of panels. For 
dead load #,= &,= 20,625 lb. The portions of the live 
panel loads supported by the left reaction are, respectively, 
6,050 + 9,900 + 7,700 + 5,500 + 3,300 + 550 = 33,000 Ib. 
No difficulty should be experienced in drawing the stress 
diagrams. 


LG: 








ANALYSIS OF STRESSES. 777 


When the stresses are obtained for each system of bracing, 
the two systems should be combined, forming the truss 
shown in the upper portion of Fig. 293. The corresponding 
stresses for the chords and for all members common to both 
systems of bracing must, of course, be added. 


1357. Formula 102, Art. 1345, may be applied at 
Peetor the stress in -@c, and at-G 2 for’ the stress in ££’. 
It will give the stresses in the two panels at each end of the 
lower chord and in the four panels at the center of the upper 
chord; i. e., in that portion of each chord where the two 
systems act as one system. 


EXAMPLES FOR PRACTICE. 


1. For the system of bracing shown in (a), Fig. 293, having all loads 
and dimensions as given above, construct the stress diagram for the 
dead load stresses. 


2. Correct the stresses as thus obtained for the vertical members. 


Notre.—Correct the stresses obtained in 74 and 4’ d' for this system 
by one-third of ove-hal/f panel load for each. Do the same in the 
solution of Example 6, thus making the sum of the corrections for 
each member in both systems equal to one-third panel load. 


3. For the same system of bracing, compute the live load stress in 
the chords and end posts from the corresponding dead load stresses. 


4. For the same system of bracing, construct the combined dia- 
grams for the maximum live load web stresses. 


5. For the system of bracing shown in (4), Fig. 293, having loads 
and dimensions as above, construct the stress diagram for the dead 
load stresses. 


6. Correct the stresses thus obtained for the vertical members. 


7. For the same system of bracing, construct the stress diagram 
for the live load stresses in the chords and end posts. 


8. Check the stresses obtained in the solution of the preceding 
example by computing them from the corresponding dead load stresses. 


9. For the same system of bracing, construct the combined dia- 
grams for the maximum live load web stresses. 


10. Mark the stresses obtained in the solution of the preceding 
examples upon the respective members in the left half of a diagram of 


178 ANALYSIS OF STRESSES. 


the truss similar to Fig. 293 (without dotted lines), adding the respec- 


tive stresses for those members which are common to both systems of 
bracing. 


Live Load Stresses. Dead Load Stresses. 
For a £2 + 81,160 1b. ( + 50,780 Ib. 
For BC + 79,200 1b. + 49,500 lb. 
For C D+ 99,000 1b. + 61,880 Ib. 
For DE + 112,200 1b. + 70,130 1b. 
For £ F + 118,800 lb. + 74,250 lb. 
For / G + 118,800 Ib. + 74,250 Ib. 
For a 6 — 386,300 lb. — 22,690 lb. 
For 6 ¢ — 36,800 lb. — 22,690 lb. 
Forc dad — 52,800 lb. — 33,000 Ib. 
For d e — 19,200 1b. — 49,500 Ib. 
For e f — 99,000 lb. — 61,880 lb. 
For f g — 112,200 lb. — 70,180 Ib. 

Ans.{ For 24 — 13,2001b. Ans. — 5,500 Ib. 
For Bc — 387,510 lb. — 23,060 Ib. 
For Aad — 88,110 lb. — 23,330 Ib. 
For Cc + 22,550 lb. + 15,130 1b. 
For Ce — 81,890 lb. — 17,500 Ib. 
For Dd + 17,050 Ib. + 11,000 Ib. 
For Df — 24,110 Ib. — 11,670 lb. 
For He + 13,750 Ib. + 6,880 lb. 
For & g — 19,440 lb. —- 5,830 Ib. 
For / f + 9,350 Ib. -- 2,750 Ib. 
For F f’— 18,220 lb. — 0,000 Ib. 
For G g + 3,030 Ib. + 2,750 lb. 

[ For Ge’ — 4,280 lb. — 0,000 lb. 


11. By formula 102, Art. 1345, verify the stress in ac (ad and 
fcjandin LL’ (£4 Fand FC). 


THE BALTIMORE TRUSS. 


1358. A form of truss will now be noticed that affords 
economical inclinations for the diagonal members, and for 
long spans retains the economical features of the Whipple 
truss, without ambiguity of stress. The truss shown in 
Fig. 294 embodies the feature known as the divided panel. 
It will be noticed that it issimply a Pratt truss in which, by 
means of an additional short diagonal member, each original 
panel is divided intotwo panels of one-half the original panel 


ANALYSIS OF STRESSES: wT9 


length; the shorter panels thus obtained are called sub- 
panels. This form of truss is known as the Baltimore 
truss. The stresses will be analyzed for a truss of this 
Ly pe. 

The data assumed will be the same as those assumed for 
the Whipple truss of the preceding pages; namely, span, 
tJsetecta number or paneis7-12- panel; length, 16.5: feet: 
height, 33 feet; clear roadway, 20 feet; live and dead loads 
per lineal foot, 1,600 and 1,000 pounds, respectively. 


- 





1359. The Dead Load Stresses.—A stress diagram 
for the dead load is also shown in Fig. 294. For one truss 
LUQUE Loe 


the panel load is 5 ss oo. Lb as before. «By 





8,250 X 11 
oe 
The loads and reactions are laid off upon the load line in 
the usual manner; thus, 1-2-3-4-5-6-7-8-9-10-11-12-13-1 is the 
load line. It will be found convenient to divide each panel 
load into two equal parts. 

For joint a, the polygon is 7-2-14-1; for joint 6 it is 
1§-14-2-8-15, and for joint 4, it is 1-14-15-16-1. Of the 
forces acting upon joint C, 1-16, or the stress in # C, is ap- 
parently the only known force, leaving three unknown 
forces, 16-17, 17-20, and 20-1, acting upon this joint. Like- 
wise, for joint c, of the three forces acting in Cc,c D, 
and c dad, none have yet been obtained by the stress diagram. 
However, from an inspection of the diagram of the truss, it 
is evident that the hip vertical C c supports one-half of each 
of the panel loads at 6 and d, besides the entire panel load 
at c, or two panel loads inall. Knowledge of this fact de- 
termines the length of the line 76-77, common to the poly- 
gons for joints C and c; andas this leaves but two unknown 
forces acting upon each joint, the polygon for both joints 
can be drawn. Again, it is evident that the stress in D, ¢ 
equals that in 4, c, and that the stress in cd equals that 
in Oc; therefore, by retracing the lines 16-15, 15-3, and 3-4, 
the lines 4-18 and 18-17 may be drawn, respectively, 

LQ. lf,—t 


formula 89, Art. 1293, R, = Rk, = = 45,375 Ib. 


780 ANALYSIS OF STRESSES. 


parallel toc dand PD, c, but equal to 15-3 and 16-15, respec- 
tively, leaving 17-16 as the closing line of the polygon for 
joint c. 

A similar difficulty will be met with in the polygons for 





FIG. 294 


joints Lande. But by noticing that the stress in /, ¢ is 
equal to the stress in Yc, or, in other words, that the 


ANALYSIS OF STRESSES. 781 


vertical component of the stress in /, ¢ is equal to one-half the 
panel load 6-7 at f, the polygon for joint e may be drawn. 
The lines 20-19, 19-5, and 5-6 are retraced, and @ line of 
indefinite length 6-22 is drawn parallel to e f; by drawing 
the horizontal line 2/7’-27 through the point 2/’, which, on 
the load line, divides the load 6-7 into two equal parts, and 
a line 20-21 through the starting point 20, parallel to £ eg, 
the length of the line 21-20, representing the stressin £ e, 
will be determined, and the polygon 20-19-5-6-22-21-20 may 
be completed for joint e. 

Thus, the slight difficulty resulting from the additional 
member necessary to the divided panel is readily overcome; 
no other difficulty will be encountered in the construction 
of the stress diagram for the dead load stresses. It is 
evident that no dead load stress will obtain in the diagonals 
Ff Gand G/F’, andthat the stress diagram will give no dead 
load stress for G g. 

The stresses for the members /, 6, ), d, and /, fare each 
to be corrected by 4 panelloadas usual. But the stresses for 
Eeand Gg are each to be corrected by 4 of 2 panel loads, = 
2 panel load, and the stress for Cc is to be corrected by 4 
of 14 panel loads, = 4 panel load; the reason for this is 
obvious. 


1360. In trusses of this type the stresses in the upper 
chord may be verified by applying formula 102, Art. 
1345, at the main vertical members, as at / e and Gg, 
taking # and mm’ equal to the number of suwb-panels at the 
left and right, respectively. The stress C, in any portion of 
the lower chord will have the following value: 


o, 
By = Gs Een (1 4.) 
in which C,, P, f, and # have the same values as in formula 
102, Art. 1345, except that if the height of the truss 
varies, will represent the height at the vertical post at the 
left (towards end of truss) of the double panel. C), equals 
the corresponding stress in the upper chord. 


182 ANALYSIS OF STRESSES. 


EXAMPLES FOR PRACTICE. 
{. For the truss shown in Fig. 294 and the dead load assumed as 
above, construct the stress diagram, determining the dead load 
stresses. 


For a B, +. 64,170 1b. For £ é 1.8. 250 IDs 
For 276 + 58,840 lb. Borg + 0,000 lb. 
onc. + 66,000 Ib. PoreA;¢, 232, : 
eet For £ G 4="74 250 1b, J Fie + 5,830 1b. 
For -aé, bc, cd, de: — 45,380 1b. «| For C D, — 35,000 lb 
For ef and / ¢ — %0,130:1b: For Die — 29° 170-15 
For B, 6, Did, Fif — 8,250 lb. For £ /, —.11,670 Ib. 
For C ¢ — 16 0016. Her i. 2: — 5,830 Ib. 


2. Correct the stresses in the vertical members. 
For B, 6, D, d, and /, f — 5,500 Ib. 


tev BoriGarc — 12,380 lb. 
le Hore eee 18,450 1p: 
For G g + 5,500 Ib. 


8 Check the stresses in the chords by formulas 102 and 104. 


1361. The Live Load Stresses.—For the chords 
and end ae the live load stresses will be most easily 






a 
Scale 1=40000 lbs . 





1 24, 28, 24; 20,24. 206 
FIG. 295. 


ANALYSIS OF STRESSES. 783 


obtained by multiplying the corresponding dead load 
1,600 
TQOQ 
For the maximum live load web stress the combined 
diagrams may be constructed in much the same manner as 
previously explained. The left reaction and that portion 
of each panel load supported by it are laid off in order upon 
the load line, and from the bottom of the load line the 
amounts of: dead load which cause negative shear in the 
panels at the right of the center are laid off upwards. The 
portions of the respective panel loads supported by the left 
reaction are found as usual by computing the reaction. 


Thus, &, = 13200 +H +#t+tetetetet+ 
+3, + 5 + 7s) = 12,100 + 11,000 + 9,900 4+ 8,800 + 7,700 
+ 6,600 + 5,500 + 4,400 + 3,300 + 2,200 + 1,100 = 72,600. 
On the load line of Fig. 295, 1-2 = 72,600 lb. is the reaction 
for a full load, and /-2-14-/ is for this load the polygon for 
joint a, giving 74-1 as the maximum stress inas,. As 
one-half the load at @ is carried by 4,¢ to the joint c, this 
condition of load will also give the maximum stress in /, C. 
For in this condition the stress in 4, 6 equals the panel load 
at 6, and by making /4-/4 equal to a panel load, the polygon 
1-14-15-16-1 is drawn for joint 4,, giving 16-2 as the stress 
in 5,C; while by removing the load from #6, 1-3 becomes 
the reaction, and, there being no stress in either 4, d or 
Lc, 1-16, represents the stress in the end post for this con- 
dition, uniform from a to C. The stress /-/6, 1s less than 
the stress 7-176. For the maximum shear in the panel cd 
and the maximum stress in C J), the loads at 6 and c must 
be removed. ‘There being now no external force between 
a and d, 1-4 represents the reaction and /-4-16,-1 is the force 
polygon for joint a. As no forces are now acting in 4,6 or 
£,¢, the polygon for joint 2, is the straight line 7-16,. It is 
known that the member C¢ supports one-half the panel 
load at @, which by the member Yc is transferred to joint 
c; therefore, by making /6,-17, equal to one-half panel load, 
i.e., the stress in Cc, the polygon 1-16,-17,-20,-1 can be drawn 
for joint C, giving 17,-20, as the maximum stress in C D,. 





abe we AD : 
stresses by the ratio —., which in this case equals 


? 





784 ANALYSIS OF STRESSES. 


If, instead of the strut D, c,a tie D, & were used to effect 
the divided panel, this condition of load would also give 
the maximum stress in D: 4 But such is not the case 
when the panel is divided by means of a strut which carries 
the load towards the reaction. For in this condition, i. e., 
with d loaded, 20,-17,-18,-19,-20. is the polygon for joint 
D,, giving 19,-20, as the stress for 1), e. By removing the 
panel load from joint d@, 1-5 becomes the reaction; as in 
this condition of load the members BZ, b, B, c, Cc, D, c, and 
D, @ carry no stress, the polygons for joints 4, and D, 
are simply straight lines, and the entire space between the 
end post a C and the diagonal C e is designated by the 
numeral 19. The polygon for joint @a is 1-5-19,-1, and for 
joint C it-is 1-19,-20,-1; the stress in D., ¢ represented for 
this condition by 19,-20, is found to be greater than as 
represented by 19,-20... 

The maximum stress in & e obtains with the condition 
giving the maximum stress in & /, that is, with the load 
at ealso removed. For this condition, 7-6 is the reaction, 
1-6-19-1 is the polygon for joint a, and 1-19,-20,-1 is the 
polygon for joint C. For joint e, 20,-19, and 19,-6 are re- 
traced, leaving the three memberse /, /, ¢, and & e¢ connect- 
ing at ¢,in which the stresses have not been determined. 
But, as has been explained for D, c, it is evident that the 
vertical component of the stress /, ¢ is equal to one-half 
the panel load at f’ Therefore, from 6, a line of indefinite 
length, as 6-22,, is drawn parallel to e f, and from the 
starting point 20, the line 20,-21 is drawn upwards (or back- 
wards in the polygon) parallel to & e; the intersection of 
these two lines is at 27. By laying off one-half panel load 
downwards from this intersection, the point 2/, is located; 
and by drawing through 2/, a line 21,-22, parallel to e /, 
intersecting the line 6-22, the polygon 20,-19,-6-22,-21,-20, 
may be completed for joint ¢, giving 2/,-20,as the maximum 
stress in Ae, For joint A, 1-20,-21,-24,-1 is the polygon, 
giving 21,-24, as the maximum stress in & F, 

For the maximum stress in /, g, the panel load at / is 


ic? 
also removed. Since for this condition no external force 


ANALYSIS OF STRESSES. 785 


is applied between @ and g, all that portion of the truss 
at the left of / ¢ may be considered to be removed, and the 
two members a / anda g substituted. The reaction for 
this condition is 1-7; for joint a, 1-7-23-1is the polygon, and, 
as the members /, ¢ and /, f have been removed, the poly- 
gon 1-23,-24,-1 gives 23,-24, as the stress in & g for this 
een: or the maximum stress in /, ¢ 

For the maximum stress in G /, and in G g¢ the load at 
g is also removed. The members a / and a g are still 
considered to be substituted for all portions of the truss at 
the left of & g. For this load 1-8 is the reaction; the poly- 
gon for joint @ is 1-8-23,-1; for joint # it is 1-23,-24,-1. 
For joint g the polygon 24, -23 -8-26,,-25,-24, 18 eBnacdcied 
in the same manner as ae laid ae joint ¢; and for joint 
G, 1-24,-25,-28,-1 1s the polygon. But the panel g /’ is at 
the right of the center, and the dead load shear in this 
panel must be deducted from 24,-25, and from 24,-2/, in 
order to obtain the correct stresses in Ggand G/.. If 
from the negative dead load numeral 8, on the load line, 
corresponding to the numeral 8 below the panel g /’, the 
horizontal line 8,-28, be drawn, it will cut off the negative 
shear in the panel ¢ /’, and the lines 24,-25, and 24,-28, will 
remain as the stresses in G gand G /,, respectively. 

For the maximum tension in /, ¢’, caused by positive 
shear, the load at f’ is removed. For this condition 7-9 on 
the load line represents the reaction. As the live load 
eget aes 9 falls below the corresponding dead load numeral 

9,, there can be no resultant positive shear in the corre- 
sponding panel /’ e’, and, therefore, no tension in /, eé’. 


EXAMPLES FOR PRACTICE. 


1. From the corresponding dead load stresses compute the corre- 
sponding live load stresses in the cnords and end posts of the bridge 
just considered. 


For a £2, + 102,670 lb. For ad, bc, cd,and de 
A For B, C+. 93,8380 Ib. — 72,600 lb. 
ns. 
For C £ + 105,600 tb. For ef and / g — 102,200 Ib. 


For £ G + 118,800 lb. 


786 ANALYSIS OF SPRESaEs. 


2. By formula 102, Art. 1345, and formula 104, Art. 1360, 
check the stresses obtained for the chords in the solution of the pre- 
ceding example. 


8. For the same bridge construct the combined stress diagrams 
determining the maximum live load web stresses. 

For a £&, + 102,670 Ib. 

For 4, C + 93,330 Ib. 

For C ¢— 26,400 Ib. 

For CD), — 60,670 Ib. 

5 For JD, e— 56,000 Ib. 

For £ e+ 24,200 Ib. 

For & /, — 34,220 Ib. 

For /y g— 82,670 Ib. 

For G g+_ 5,780 lb. 

For G /,—_ 8,170 Ib. 
For 2, 6, D, d, and 

For /, f/f — 18,200 Ib. 
Por bic eipen in 

For 7; e+ 9,380 Ib. 


Ans. 


THE PETIT TRUSS. 


1362. <A modified form of the Baltimore truss is shown 
‘in Fig. 296. The general form of the truss is the same 
as that of the truss shown in Figs. 294 and 295; but, except 
in the end panels, the additional diagonals employed to 


Fic. 296. 


subdivide the panels are ties instead of struts. The fea- 
ture of subdividing the panels by means of additional ties 
is called the half hitch, and the ties so used are some- 
times called sub-ties. The half hitch does not give as 
good economy as is obtained when the subdivision is 
effected by means of a strut, and the diagonal web members 
thus connected are also susceptible of greater vibrations, 


ANALYSIS OF STRESSES. 787 


but it is very commonly used. As subdivided panels 
and curved chords are both well adapted to long spans, 
these two features are usually combined. When the panels 
are subdivided, either by means of struts or ties, in a truss 
having curved chords, the truss is usually known as the 
Petit truss; it is one of the most economical forms ofa 
simple truss for long spans. The general form of the Petit 
truss commonly used for highway bridges, together with 
the stress diagram for the dead load stresses in the same, 
is shown in Fig. 297. The stress diagrams for this truss 
will serve as general illustrations of the graphical analysis 
for half-hitch trusses. It is evident that the panels could 
have been subdivided by means of struts instead of ties. 
In the two end panels this truss differs materially from 
those shown in Figs. 291 and 292; the hip is at 4 instead of 
at C, and C¢ is a compression member instead of a tension 
member. The portions of the truss between @andc and 
between a’ and c’ are similar to the corresponding portions 
of a Pratt truss, while between c and c’ the panels are sub- 
divided. 

Except in regard to height, the data assumed for this 
truss will be the same as for the Whipple truss and the 
Baltimore truss in the preceding articles; namely, length of 
span, 198 feet, divided into 12 panels 16.5 feet long each; 
clear width of roadway, 20 feet; live and dead loads per 
lineal foot, 1,600 pounds and 1,000 pounds, respectively. 
The heights of the truss at the hip vertical and at the inter- 
mediate posts, in order towards the center, are 22, 28, 33, 
and 33 feet, respectively. 


1363. The Dead Load Stresses.—for each truss 
the dead load per panel is 8,250 pounds, and &, = KX, = 45,375 
lb., as before. The loads and reactions are laid off in order 
upon the load line in the usual manner. No difficulty should 
be experienced in drawing the stress diagram for the dead 
load. The force polygons for joints a, 6, b,c, and C are 
constructed as for an ordinary Pratt truss with curved 


chords, 1-16-17-18-1 being the polygori for joint C. For 


788 ANALYSIS OF STRESSES. 


joint @ the polygon is 17-4-5-19-17; for joint D,, it is 
18-17-19-20-18; for joint e, it is 20-19-5-6-21-20; and for 
joint A, it is 1-18-20-21-22-1. Further explanation is un- 





a 
1, 2b63¢ 4d 5@ CF 79D S Ff'9 10d Cc’'12 b'13 
LIGS 





Ww 
Scale 1=250001b6s. 





oe Sane 
FIG. 297. 
necessary; the entire stress diagram will be readily under- 
stood. . 
In correcting the stresses for the vertical members, the 
stress for 4 O is corrected by $ of 1 panel load, the stresses 
for / e and G gare each corrected by 4 of 2 panel loads, or 


ANALYSIS OF -STRESSES. 789 


2 panel load, while the stress for Cc is corrected by 4 of 
14 panel loads, or 4 panel load. 

In half-hitch trusses the stress obtained for the lower 
chord may be verified by applying formula 102, Art. 
1345. Where the upper chord is horizontal, its stress 
will have the value of C, in formula 104, Art. 1360. 
Where the upper chord is not horizontal, C, will represent 
the horizontal component of its stress; the stress may be 
found by substituting the value of C, for ©, in formula 
103, Art. 1346. Where the height of the truss varies, 
use for 4 in formula 104 the height at the vertical post at 
the right (towards the center of the truss) of the double 
panel. 


EXAMPLES FOR PRACTICE. 


1. For the truss shown in Fig. 297, the data being as above, con- 
struct the stress diagram determining the dead load stresses. 


For aB + 56,720 Ib. ( For. Ce, + 11,200 Ib. 
For BC + 51,730 1b. | For C D, — 28,210 Ib. 
Ans. 4 For CE + 70,930 lb. 4 For D, e — 21,830 Ib. 
For EG + 78,380 lb. For D, E — 5,460 Ib. 
Foraéandéc —34,0301b. | For £ e + 5,880 Ib. 
Forcdandde — 48,620 lb. For E F; — 17,500 Ib. 
For efand/ ¢ — 66,000 lb. | For % g — 11,670 Ib. 
ANS.) For Bb, Dd. Fi f — 8,250 Ib. | For 4 G — 5,830 Ib. 
For Bc — 24,310 lb. | ForG g — 8,250 lb. 


2. Correct the stresses for the vertical members. 
For Bb, D, d, and -y f — 5,500 Ib. 


Ror Cor + 15,330 Ib. 

POE 
Mone Vette oe + 11,380 Ib. 
For Gg + 13,750 lb. 


1364. The Live Load Stresses.—For one truss the 
panel live load is 13,200 pounds. The maximum live load 
stresses in the chords and end posts may be found by multi- 


plying the corresponding dead load stresses by the ratio ue 


as previously explained. The maximum live load web stresses 
may be obtained by constructing the combined stress 


790 ANALYSIS OF STRESSES. 





diagrams as shown in Fig. 298. A,= 13,200x (444+ 12+44+ 
Bette tay toast tet ee te t+ 2) = (12,100 411,000 + 
9,900 + 8,800 + 7,700 + 6,600 + 5,500 + 4,400 + 3,300 + 
2°00: 1,100) = 72,600" Ib. From 1-2 7 ielareee 
upwards, and 2-3 = 12,100 Ib’, 3-4 = 11,000 1b “etc are laid 
off downwards tothe starting point. Alsofrom 7, 7,-8,, and 
&,-9,, equal, respectively, tothe amount of negative dead load 
shear produced at the right of the center by the dead loads 
at g and /", allinthe usual manner. No difficulty will be en- 
countered in constructing the diagrams, but some irregu- 
larity will be noticed in the conditions of loading which 
produce maximum stresses 1n certain members. 

With the truss fully loaded, 1-2 represents the reaction, 
and the polygon 1-2-14-1 for joint a gives the maximum 
stresses ina@dandas. For the maximum stress in # ¢ the 
load at 6is removed; J-3 is the reaction for this condition 
and 1-3-15,-1 is the polygon for joint a; as there is no stress 
in B 6, 1-15,-16,-1 1s the polygon for joint 4; giving 15,-16, 
as the maximum stress in /e. 

The maximum stresses in Cc, C D,, and DJ, e occur with no 
loads upon 6 and c, all other joints being loaded. For the 
stresses in C DD, and J. e, considers members 2 C-andiae 
to be substituted for those portions of the truss at the left of 
Candd. The reaction is 7-4; 1-4-17,-1 is the polygon for 
joint a, and 1-17,-18,-11s the polygon for joint C, giving 17,-18, 
as the maximum stress in C J). Onthe load line, 4-4, is laid off 
downwards equal to the full panelload at d; 17,-4-5,-19,-17,1s 
the polygon for joint @, and 18,-17,-19,-20,-18, is the polygon 
for joint ),, giving 19,-20, as the stress in D, ¢ and 20,-18, 
as the stressun D4. “That the 6tréss ing 2 within ore 
loaded is greater than with that joint unloaded may be 
readily shown. With no load at d 1-5 becomes the reaction, 
1-5-19,-1 is the polygon for joint a, and 1-19,-20,-1 the poly- 
gon for joint C, giving 19,-20, as the uniform stress from C 
to e for this condition; it is found to be less than 19,-20.. 
By considering the original portions of the truss to be 
restored to the irrespective positions, the reversed polygon 
TIS 17 1641 Gives 10, 17 as the stresssin tae. 














£20000 Ibs - 


Scale 1 


15, 





\ 
\ 
st 
\ 
\ 
\ 


a 
Ry 





oan 


“p yeeceng ic eg 
e 


2 


298. 


FIG. 


ANALYSIS OF STRESSES. 791 


For the maximum stresses in / /, and /’, g, all joints at the 
right of the panel ¢ fare loaded, no load being at the left of 
that panel. The members a £ and e fare considered to be 
substituted for all portions of the truss at the left of / and /. 
For this load, 1-6 is the reaction, and, by proceeding as 
before, 21,-22,, 28,-24,, and 22,-24, areobtained as the maxi- 
mum stresses in / /(, / g and /, G, respectively. By con- 
sidering the original members of the truss to be restored, and 
drawing the reverse polygon for joint /, 20,-27 is obtained 
as the stress in & e for this condition of load. 

But this is not the maximum stress in this member; for it 
will be found that with all joints to the right of the panel 
e f loaded, an additional load placed upon joint @ will increase 
the stressin / e. As 1-6 represents the reaction with all 
joints at the right of the panel e floaded, and the others un- 
loaded, to obtain’the reaction with the additional load at d, 
lay off upon the load line above 6 the amount 4’-6, equal to 
4-5 (i. e., equal to the amount of the left reaction produced 
by the load at @); J-4' is the left reaction from all the loads 
upon the truss in this condition. 

Considering a C andadto be substituted for those por- 
tions of the truss at the left of Cand d, the polygon 1-4'-17'-1' 
is obtained for joint a, 1-17’ 18'-1 is obtained for joint C, 
17'-4'-5'-19'-17' for joint d, 18’-17'-19'-20'-18' for joint D,, and 
20'-19'-5'-21'-20' for joint e. The stress 20’-21' for & e is 
found to be greater than the stress 20,-2/,; it is the maxi- 
mum stress for 4 e. For the maximum stress in G /, all 
joints at the right of the panel ¢ /’ are loaded, no load being 
at the left of that panel. For this condition 7-8 is the re- 
action, and, with a G and a /' substituted for all portions of 
the truss at the left of G and /’, 1-8-25,-1 is the polygon for 
joint a, and 1-25,-27,-1 the polygon for joint G. In the 
panel g /f’ there exists an amount of negative dead load 
shear represented by 7-8, ; 
the horizontal line 8,-22,, the effect of the negative shear, 
or 27,-27,, is cut off, leaving 25,-27, as the correct stress 
inGF,. If stress canoccur ina member /, g, it will obtain 


2 


its maximum limit with this condition of load. The 


therefore, by drawing through 8, 


792 ANALYSIS OF STRESSES. 


negative dead load shear in the panel /’ ¢’ equals 7,-9,; the 
live load reaction is 7-8. The polygon for joint a is 1-8-26,-1, 
and for joint G it is 1-25,-27,-1. To draw the polygon for 
joint f’, retrace 25,-8, pass downwards upon the load line 
8-9', the amount of the entire panel load at /’, and with- 
out proceeding further it is found that the point 9’, as 
well as the point 9, falls below the point designated by the 
corresponding dead load numeral 9,, and, therefore, no 
positive shear can obtain in the corresponding panel 9 or 
f' e'; consequently, no stress can be produced in a counter 
VP ae 

The maximum stress in G ¢ will obtain with joint f and 
all joints at the right of the panel gf’ loaded. The amount 
6'-8 = 6-7 is laid off upon the load line above & ;. 1-6’ is the 
reaction for this condition. With a ~ and a / substituted 
for those portions of the truss at the left of Zand /, 1-6'-21'-1 
is the polygon for joint a. For joint & the polygon is 
1-21'-22'-1; for joint / it is 21'-6'-7'-28'-21'; for joint F, it is 
22' 27'-23'-24'-22', and for joint g it is 24’-23'-7'-25'-24'. 

The line 25'-24' would represent the live load stress in G g, 
if no negative dead load shear existed in the panel ¢ f’; but 
as the stress in G g is produced by the stresses in /, G and 
f G, the same amount of negative dead load shear must be 
deducted from the stress 25'-24', obtained for G g, that was 
deducted from the maximum stress previously obtained 
for G /,. This negative shear is represented by 7,-8,, and a 
convenient method of deducting it is to consider the stress 
in & F, to be represented by 21'-22, instead of 21'-22'; then 
22,-21'-23'-24,-22, becomes the polygon for joint /, and 
24,-23'-7'-25,,-24, the polygon for joint g, giving 25,-24, as 
the correct maximum stressin Gg. The stress in each sus- 
pender 4 0, PD, d, and /, fis tension equal to the panel of 
live load supported by it. 

It is evident that the maximum stress produced in G /, 
by the right reaction will be the same asthe maximum stress 
in G /, due to the left reaction. Therefore, both members 
must be given the greater stress found above for either of 
these members. 


ANALYSIS OF STRESSES. 793 


EXAMPLES FOR PRACTICE. 


1. From the data given for the truss shown in Figs. 297 and 298 
and the dead load stresses previously obtained for the same, compute 
the live load stresses in the chords and end posts. 

For a £+ 90,750 Ib. 2 
Rota Co Gaia ee ss Bee 


For C E+ 113,480 1b. For cd and d Xe re 
For EG + 125,400 1b. For e f and / 2 — 105,600 Ib. 


2. Construct the combined stress diagrams for the maximum live 
load web stresses for the same. 


Ans. 


( fora B + 90,750 Ib. For D, e — 44,670 Ib. 

For a 06 — 54,450 lb. For D, E — 10,070 lb. 

For Bb, D, d, For £ e + 22,770 lb. 

Ans. ~ and /; f — 13,200 Ib. For £ F, — 43,560 lb. 
For Bc — 43,220 lb. For /, ¢ — 34,220 lb. 

For C ¢ — 28,290 Ib. For G g + 13,480 Ib. 

Horo — 53,320 Ib. [ For 72 G= /, G — 17,500 lb. 


38. Check the chord stress obtained in the solution of Example 1 
above. 


ERROR IN THE ASSUMPTION FOR MAXIMUM 
WEB STRESSES. 

1365. Throughout the foregoing investigation of the 
stresses in trusses it has beenassumed that each loaded joint 
receives its panel load wholly independent of the load upon 
any other joint; for uniform loads this is the usual assump- 
tion and practice. The assumption is not exactly correct, 
as may be seen from an inspection of Fig. 290. We have 
assumed that it is possible for joint c, for example, to be 
fully loaded with a whole panel load, while 4 was unloaded; 
but, in reality, in order that c may carry a full panel load, 
the panels 6c andc d must be loaded, half of the load on 
each going toc; were cd loaded and éc unloaded, ¢ would 
carry only one-half of a panel load. But, then, with 6 c 


1 é 
loaded, % carries half a panel load (= 5-/, calling P the 


panel load). The reaction 4,’ will be what we have found 
it when J was assumed to be unloaded (A), plus the part of 


the =P carried py 0, which goes to the left support; that 


794 ANALYSIS OF STRESSES. 


aes estates 
1S, R, = ae -|- 8 x oy 
of being &,, as assumed, will be #,’, which acts upwards, 


; and the shear in the panel @c, instead 


sme 
minus —, which acts downwards at 0; that is, shear = RX,’ — 


Ve: i Visipi 2 se  easeere, ro: 
Fete ge yg a ane As this is smaller 


than #&,, the corresponding stresses will be smaller than 


T 
9 6 
12375 lbs. 7 1237 lbs. 





Sy 


¢ 


Ped en uy eens 
o 


-239831D3.-". 





, 


——19 


sa nc I a | La 1 penis 1 iol PE FE pea 


Pe 


6806 lbs, 


8 
ar) 
: 
a 


FIG. 299. 


those we have found, and the members also smaller. By 
neglecting the load at 4 the members are, therefore, made 
larger than they actually have to be. As the error is both 
small and on the side of safety, it is usually disregarded, as 
we have done. 


ANALYSIS OF STRESSES. 795 


STRESSES IN A BRACED PORTAL. 

1366. In Arts. 1309 to 1314, the method of obtain- 
ing the stresses in a latticed portal by means of moments 
was explained. Butin certain cases it is desirable to con- 
struct other forms of portals. The Whipple truss, shown 
in Fig. 293, requires a very deep portal, and for it the form 
of portal shown in Fig. 299 is more economical than a lat- 
tited portal. This form of portal is called a braced por- 
tal. It consists of two struts L 4’ and 00’ connected by the 
two diagonal rods 4’ dand £4 UO’, called sway rods; 0 0’ is 
called a sub-strut. The widths of the end posts are not 
yet known, but the width center to center of chords may be 
approximately calculated by formula 101, Art. 1342. 
tere = 20,.and © = 20+ = 
purposes it will be convenient to take the distance center to 
center of end posts at 21 feet. ~ As the panel length is 
16.5 feet and the height of truss is 33 feet, the length of 
each end post is 4/33’ + 16.5” = 37 ft. (nearly). 

The depth of the portal 4 0 (in plane of end posts) will be 
taken at 18 feet. By applying the principles of moments to 
this portal a very easy analysis is obtained. If the wind 
pressure against the upper chord be taken at 150 pounds per 
lineal foot, the panel wind load is 150 X 16.5 = 2,475 pounds. 
As there are ten panels in the upper lateral system, the 
amount of wind pressure carried by it against each portal is 
10 —1 

2 
panel of wind load directly at the portal, one-half of which, 
or 1,237 pounds, is assumed to be applied against the wind. 
ward and the same amount against the leeward side. In 
the figure, the wind isassumed to be from the left; 11,138 + 
1,237 = 12,375 lb. is the pressure against the windward 
side, and 1,237 lb. the pressure against the leeward side of 
the portal. The horizontal and the vertical reactions at the 
foot of each end post are found as explained in Arts. 1309 
and 1310. The horizontal reaction at the foot of each 
12,375 as 1,237 _ 6,806 Ib. 





— Ab 00 tt. but tor present 








< 2,475 =11,138 lb. To this must be added the 


post is 
T. I[,—12 


796 ANALYSIS OF STRESSES. 


The amount of each so-called vertical reaction equals 
(12,375 + 1,237) x _ = 23,983 lb., positive at the foot of 
the leeward post, and negative at the foot of the windward 
post. The positions and directions of all external forces 
acting upon the portal are shown in Fig. 299. With 
the wind pressure from the left the member 4 0’ does not 
act, and need not be considered; the members 4 5’, 4 L’, and 
b b' are, therefore, the only members of the portal consid- 
ered in the following analysis. With the wind from the 
right, the opposite conditions would obtain, and the tie B 0’ 
would act instead of the tie b SB’. 





1367. In Art. 1128, it was stated that the moment of 
a force about any point in its line of action ts sero. If now 
the portal be conceived to be cut by a vertical plane ~ y, 
this plane will pass through the acting members & 4’, b B’, 
and 0 6’, each of which represents the line of action of an 
internal force. If we take moments of all the forces at the 
left of the plane about 0, the intersection of 6 4’ and b 0’, 
the bending moment thus obtained must be resisted entirely 
by the moment of the force in & 4’ about that point, 
as the moments of the forces in 0 4’ and 0 0' about O are 
zero. If then we divide the bending moment thus ob- 
tained by & Od, the lever arm of theforce 4 4’, the quotient 
will equal the internal force, “or stress, sin “654. saline: 
wise,-if we take moments about 4’, the forces in & J’ and 
b 4’ will have no rotative effect,and the bending moment 
thus obtained must be resisted entirely by the moment of 
the force in 60’; by dividing this bending moment by 
the lever arm J’ 0’, the quotient will equal the stress in 
bO'. 

This principle is perfectly general, and may be stated as 
follows: 


Wherever a truss can be conceived to be cut by a plane in 
such manner as to entirely divide tt without cutting more 
than three members, the stress in any one of the members may 
be found by taking moments of all the forces upon etther side 


ANALYSIS OF STRESSES. oe 


of the plane about the point of intersection of the other two 
members. ? 
By taking moments of the forces at the left of + y about 
b, Fig. 299, the compression in & &' is found to be 
12,375 X 18 + 6,806 x 19 — 23,983 x 0 
18 
same result may be obtained by taking moments of the 
forces at the right of xy about the same point. In this 
case the negative sign of the result will simply signify that 
the resultant moment of the forces at the right of +y tends 
to cause rotation to the left; it is plain that this will cause 
compression in £4’. The stress in 6 0’ is found by taking 
moments of the forces at the left of ry about 4’; thus, 
6,806 X 3% + 12,3875 X 0 — 23,983 X 21_ 13.9901b. Here 
18 ; 
again, the negative sign of the result signifies that the 
resultant moment of the forces at the left of ry tends to 
cause rotation to the left about 4’, which evidently pro- 
duces compression in 00’. The stress in 6 4’ could be found 
by taking moments about the intersection of £4’ and 00’, 
if those members intersected, but they are parallel and do 
not intersect. 





= 19,559 Ib. The 





1368. It is evident that the vertical shear in the portal 
at the plane + y is equal to either vertical reaction, negative 
on the left and positive on the right of the plane. As this 
shear is vertical, by laying it off upon a vertical line and 
projecting it upon a line drawn parallel to J 4’, the pro- 
jected length of the latter line will represent the tension in 
6 Bb’, It will be convenient to lay off the vertical shear 
above 6 on 6 & (produced if necessary). If 0 v is laid off by 
any convenient scale equal to the vertical shear = 23,983 
lb., then, by drawing the horizontal line vs, the line 0 s thus 
cut off will represent the stress in 6 4’. 


1369. It will be well to notice that the amount of wind 
pressure to be assumed, as applied directly at the portal, 
may, in certain cases, be more than one panel load. For 
instance, in the Baltimore truss, shown in Fig. 294, if lateral 


798 ANALYSIS OF STRESSES. 


struts "are placed only: at.C, -2."G,e2 eandec.-sanieeacy 
upper lateral tie extends longitudinally through two panels, 
as from C to £, the amount of wind pressure to be assumed 
as applied directly at C would be two panel loads. But if, 
with the lateral ties extending through two panels, the end 
post extends horizontally through but one panel, the amount 
of wind pressure to be assumed to be applied directly at the 
hip & would be one and one-half panel loads. 


EXAMPLES FOR PRACTICE. 


1. Find the stress in 6 B’, Fig: 299. Ans. — 36,850 lb. 


2. Find the stress in 2 Z’ by taking moments of the forces at the 
right of ry. 


3. Find the stress in 46’ by taking moments of the forces at the 
right of ry. 


FLOOR BEAMS WITH SIDEWALK CANTILEVERS. 


1370. When, in addition to the roadway, a bridge car- 
ries sidewalks, the latter are usually supported outside of 
the truss upon projecting or cantilever ends of the floor 
beams, usually called sidewalk brackets. <A floor beam 
having sidewalk brackets is shown in Fig. 300. 





FIG. 300. 


In estimating the dead load for a bridge having sidewalks, 
for the quantity 4, in formulas 9O and 91, Art. 1298, 
use the clear width of roadway plus the width of one side- 
walk. Also for 7 in formula 93, Art. 1315, use the 


ANALYSIS OF STRESSES. 799 


distance between centers of supports plus the width of one 
sidewalk; but for W, in the same formula, use only the live 
load upon the beam defween supports. In finding the maxi- 
mum bending moment at the support and at the center of 
the beam, find first the bending moment at each point due 
to the entire dead load; then find the bending moment at 
the support caused by the live load upon the sidewalk can- 
tilever, and the bending moment at the center caused by the 
live load upon the roadway wth no live load upon the side- 
walks. The live and dead load bending moments, as found 
for each point, should then be combined. 

The live load bending moment at the center may be 
found as for a simple beam by formula 97, Art. 1318. 
The dead load moments may be found by constructing the 
moment diagram, or by computing the resultant moment of 
all the forces at the left. 


EXAMPLE.—The floor beam of a bridge having 16-foot panels sup- 
ports a 20-foot roadway and two 5-foot sidewalks. What is the weight 
of a white oak floor for the same (a) per lineal foot of bridge, and (é) 
per lineal foot of the loaded portions of the beam ? 


SOLUTION.—(a) From Table 29, Art. 1299, for 16-foot panels the 
weight per lineal foot of a white oak floor 30 feet in width is 309.6 + 9 x 
45.6 = 720lb. Ans. (4) The total floor load upon the beam is 720 x 16 = 
11,520 1b., and the weight of the same per loaded foot of beam is 


11,520 
30 = 384 1b. Ans. 





EXAMPLE.—Assuming the live load to be 100 pounds per square foot, 
the width of each chord to be 1 foot, and the total depth of the beam 
to be 24.5 inches, what is (a) the total weight of the beam, and (é) the 
weight per lineal foot of beam ? (Assume the total weight of the beam 
to be distributed along its loaded portion.) (c) What is the total 
amount of dead load per lineal foot of beam upon the loaded portion ? 


SOLUTION.—(a) The total live load upon the beam between supports 
equals 16 & 20 x 100 = 82,0001b.= IV ; and the length of beam between 
centers of supports plus the width of one sidewalk is 21+5=26=/7, 


; : 4 32,000 «K 26 __ 
The total estimated weight of the beam is, therefore, 30245 7 
1,698 


1,698 lb. Ans. (0) “air = 56.6 lb. Ans. (See Ans. to (4) of preceding 
example.) (c) 384 + 56.6 = 440.6. Ans. 


800 ANALYSIS OF STRESSES. 


EXAMPLE.—Calling the dead load 440 pounds per lineal foot of the 
loaded portion of the beam, what is the bending moment in inch- 
pounds due to the dead load (a) at the left support A, and (4) at the 
center of the beam ? 


SOLUTION.—See Fig. 300. (a) The total dead load upon the side- 
walk cantilever is 5 x 440 = 2,200 1b. The distance between the center 
of gravity of this load and A, is 2.54 .5=8 ft. It will be remem- 
bered that the bending moment of a cantilever is negative. ‘There- 
fore, the bending moment at A, is — (2,200 x 3) = — 6,600 ft.-lb. = — 
6,600 x 12 = — 79,200 in.-lb. Ans. (6) The amount of load supported 
by A, is 2,200 + 10 x 440 = 6,600 lb. The resultant bending moment 
at the center is 6,600 « 10.5 — 2,200 x 13.5 — 4,400 x 5 = 69,300—29, 700— 
22,000 = 17,600 ft.-lb. = 17,600 x 12 = 211,200 in.-lb. Ans. 


EXAMPLE.—What is the bending moment in inch-pounds produced 
by the live load (a) at the left support ,, and (4) at the center of the 
beam ? 


SoLuTIoN.—(a) The total live load upon the sidewalk cantilever is 
5 xX 16 X 100 = 8,000 lb., and its moment about 7, is 8,000 « 3 = 24,000 
ft.-lb. = 24,000 x 12 = 288,000 in.-lb. Ans. (6) By formula 97, of 
Art. 1318, the bending moment at the center produced by the live 
load upon the roadway, with no live load upon the sidewalks, is 

20 + 2 

SE 000 (20+ *) _ 88,000 ft.-Ib. = 88,000 x 12 = 1,056,000 in.-Ib. Ans. 

EXAMPLE.-—What is the total bending moment (a) at #, and (4) at 
the center of the beam ? 


SoLuTIoN.—(a) The total bending moment at RX, is 79,200 + 288,000 = 
367,200 in.-lb. Ans. (4) The total bending moment at the center of 
the beam is 211,200 + 1,056,000 = 1,267,200 in.-lb. Ans. 


EXAMPLES FOR PRACTICE. 


1. A bridge having 15-foot panels carries one 16-foot roadway and 
two 4-foot sidewalks. What is the weight of a white oak floor (a) per 
lineal foot of bridge, and (4) per lineal foot of the loaded portion of 
the beam ? (a) 552 Ib. 

Ans. 
(6) 345 1b. 

2. Assuming the total depth of the beam to be 21 inches, the width 
of each chord to be 1 foot, and the live load upon the beam to be 80 


pounds per square foot, what is (a) the total weight of the beam, and 
(4) the weight per lineal foot of the loaded portion ? 


Ans. 


(a) 960 Ib. 
(5) 40 Ib. 


ANALYSIS OF STRESSES. 801 


3. What is the bending moment in inch-pounds produced by the 
dead load (a) at the support, and (4) at the center of the beam? 
Ans, § (@) 46,200 in.-Ib. 
( (4) 120,120 in.-Ib. 
4. What is the bending moment in inch-pounds produced by the 
live load (a) at the support, and (4) at the center of the beam ? 
anni 1 (a) 144,000 in.-lb. 
(6) 518,400 in.-lb. 


5. What is the total bending moment in inch-pounds in the floor 
beam of the four preceding examples (a) at either support, and (4) at 
the center ? A ( (a) 190,200 in.-lb. 

ns. 
( (4) 626,520 in.-lb. 


CONCENTRATED WHEEL LOADS. 


1371. The floor members of highway bridges con- 
structed in cities and manufacturing districts are generally 
designed to carry not only the specified uniform load but 
also certain specified concentrated or wheel loads, such as 
an electric car, a steam road roller, etc. In such bridges, 
metal stringers are commonly used. The bending moment 
at any point along a stringer or beam caused by the uniform 
(live and dead) load may be obtained by applying formula 
95, Art. 13173 the bending moment due to the concen- 
trated load is then found and combined with the preceding, 
in order to obtain the resultant bending moment. For 
stringers and beams of uniform cross-section, it is necessary 
to find the marzmum bending moment only. The method 
of obtaining the maximum bending moment produced by 
concentrated loads will now be explained. 

A single load upon the span will first be considered. In 
Fig. 301 is represented a single load WW in any position upon 
any span /, By Art. 



















2 
[bi ka Kee Si ee ak 
| 
Wa ——a——+——_—— 5 ——_ 
au ie For Ry, aa ant 
any position of the Fic. 301. 


load, the greatest bending moment is under the load, and 
its value is 


802 ANALYSIS OF STRESSES. 


< 
M = Ra=R,b= 9" (105.) 


The position of W that produces the greatest bending 
moment is atthe center of the beamy >In that caséy7 — gee 


ze ab =" and formula 105 becomes 


an 
2 


_ We Ww 
eed RE i 





(106.) 


Norre.—By comparing formula 105 with formula 94, Art. 1316, 
it will be noticed that a single load concentrated at the center of the 
span will produce just double the bending moment at the center of 
the span that is produced at that point by the same amount of !oad 
uniformly distributed upon the same span. 


1372. If twoor more concentrated loads are situated 
in any position upon a stringer, the bending moment at each 
point along the stringer can readily be obtained by drawing 
the moment diagram. By constructing the shear diagram 
also, the point of maximum bending moment will be located 
by the point where the shear line crosses the shear axis. 
Or the bending moment at any point may be computed by 
simply finding the resultant moment of the forces acting on 
either side of that point. 

The maximum bending moment in a simple beam, produced 
by any system of quiescent loads, occurs at a point where the 
sum of the loads at the left (including, tf necessary, a portion 
of the load directly at the point) equals the left reaction, or 
in other words, where the shear ts Zero. 


> 


1373. But the system of wheel loads under ordinary 
conditions of traffic, as an electric railway car, a road roller 
or heavily loaded truck, comes upon one end of the stringer, 
and, proceeding along its entire length, passes off at the 
opposite end, producing bending moments of varying in- 
tensity, which at some point during the passage of the loads 
become maximum. To find where this maximum bending 
moment occurs, and the position of the system of loads pro- 
ducing it, the two following principles must be observed: 


ANALYSIS OF STRESSES. 803 


L, The maximum bending moment will occur under a load. 

IT. The center of the span will be midway between the point 
of maximum bending moment and the center of gravity of the 
system of loads. 


If all the loads belonging to the system are not upon the 
span at the same time, the center of gravity of those loads 
which are upon the span must be taken. When the posi- 
tion of the loads producing the maximum bending moment 
is found, the bending moment can be obtained either by 
calculation or by drawing the moment diagram. 

In the case of two unequal loads upon a stringer (or any 
other simple beam), the maximum bending moment will 
occur under the heavier load. Let &, be the reaction on 
the same side as that on which the heavier load rests, lV, 
the weight of this load, WV, the weight of the smaller load, a 
the distance between the loads, and / the length of the 
stringer (or beam). Thus the distance + from X&, to W, is 
given by the formula 





eee l a 
Phage W (107.) 
(1477) 
If W, = W,, then 
ee 


In the latter case it will be noticed that the postition of the 
loads ts independent of those loads, that is, whatever the 
loads may be, if they are equal, the fosztzon for maximum 
bending moment is always the same, so long as the length 
of the beam and the distance between the loads remain 
unchanged. 


EXAMPLE.—It is assumed that the floor system of the bridge truss, 
shown in Figs. 297 and 298, carries an electric railway track, and that 
stringers are so arranged that each track rail is supported directly on 
top of a stringer. The car and its entire load, assumed to weigh 
16 tons, is supported upon four wheels, each of which is assumed to 
carry one-fourth of the load, or 8,000 pounds’ the two wheels upon 
either track are 7.5 feet apart, center to center. What is the position 


S04 ANALYSIS OF STRESSES. 


of the wheels upon the stringer which will produce the maximum 
bending moment ? 


SoLuTION,—The span of the stringer is equal to the panel length of 
the truss, or 16.5 feet. 


Ss s Here, 7= 16.5, a=.5, 

Ss = and W, —= W, = 8,000 

S S lb. Then, formula 108 
Lee / i?) ; 3 

| 15 — gives a ee 


6.575 ft) ‘Distance at 
W, from center = 7.5 
— 6.375 = 1.875, which 


; u 7.5 
1S ape ye OTF oOnec- 








FIG. 302. 


half the distance be- 
tween WW, and the center of gravity of the system, as stated in II. 
See Fig. 302. 


1374. With three loads upon the span, if the loads 
are equal, or if the center load is the greatest, the maxi- 
mum bending moment will occur under the center load. 
If the two outer loads are equal and are at equal dis- 
tances from the center load, the maximum bending moment 
will occur when the center load is at the center of the 
span. 

As the number of loads increases, the problem becomes 
more complicated, especially if the magnitudes of the loads 
vary.. It may always be solved, however, by applying the 
above conditions to the several wheels, the maximum _bend- 
ing moment being usually found under one of the heavier 
loads near the center of the system. In case of a stringer 
or floor beam of uniform cross section it is necessary to 
obtain only the one absolutely maximum moment; in such 
a case little, if any, difficulty will be experienced. 

It must be noticed that formula 107 (and the same 
applies to 108) gives the position for maximum bending 
moment when the two loads are actually upon the span, but, 


when a is greater than & it may happen that this bending 


/ 


/ 
moment is less than ri , or the center bending moment 





ANALYSIS OF STRESSES. 805 


with only W, upon the span. Insuch a case, both moments 


1 


should be calculated to see which is the real maximum. 
Furthermore, the value of + given by formula 107 may 
be so great as to make it impossible for JV, to be upon the 
span when IV, is at the distance + from &,. This happens 
1 


an W,). In this case, 


whenever @ is greater than iC ae 
Ane 





eer We 1° 
the center bending moment v6 is to be taken as the 


maximum. 


EXAMPLES FOR PRACTICE. 


1. With the loads of the above example in the positions shown in 
Fig. 3802, what is the value of A, ? Ans. 6,182 Ib. 


2. What is the maximum bending moment produced by the same? 
Ans. 39,410 ft.-Ib. 

3. With the loads in the same position, find the bending moment 
under the right wheel /1,. Ans. 25,773 ft.-lb. 


4. Assuming the span of the stringer to be 20 feet, what is the 
position of the same loads producing maximum bending moment ? 

Ans. With either load 8.125 feet from the corresponding end of the 
stringer. | 


5. What is the maximum bending moment for the conditions of the 
preceding example ? Ans. 52,813 ft.-lb. 


6. Assuming the span of a stringer to be 18 feet, the two loads 
upon it to be 9,000 and 6,000 pounds, respectively, and the distance 
between the loads to be 11 feet, find the position at which the maxi- 
mum bending moment will occur, both wheels being upon the span. 

Ans. Under the heavier load at a distance of 6.8 feet from the 
nearer end, or 2.2 feet from the center of the span. 


7. For the conditions of the preceding example, what is the maxi- 
mum bending moment ? Ans. 38,533 ft.-lb. 


8. With the same span and loads as in the two preceding examples, 
and with the heavier load at the center of the span, what is the 
maximum or center bending moment ? Ans. 40,500 ft.-lb. 

9. With the same loads, but with a span 24 feet in length, what is 
the bending moment with the heavier load at the center of the span ? 

Ans. 57,000 ft.-Ib. 


10. With the same span and loads as the preceding example, what 
is the maximum bending moment ? Ans. 60,025 ft.-lb. 


806 ANALYSIS OF STRESSES. 


CONCLUDING REMARKS, 


1375. There are several forms of bridge trusses which 
have not been noticed in the preceding pages. The forms 
of trusses for which the stress diagrams have been explained 
are those modern forms of simple trusses most commonly 
constructed in this country at the present time; they are 
thought to be representative and typical of approved modern 
practice. 

Other methods are employed for obtaining the stresses in 
framed structures; the method which has been explained 
and generally followed in the preceding pages is believed to 
be the most systematic, flexible, and accurate, as well as the 
most clear and popular graphical method. ‘The principles 
on which the method is founded are general, and the student 
will have no difficulty in applying them to any ordinary 
truss. 

The examples that have been explained have been given 
solely for the purpose of illustrating the application of gen- 
eral principles and the methods to be employed. ‘The design 
of a bridge must, of course, depend largely upon the phys- 
ical conditions peculiar to the location and other special cir- 
cumstances; so that, in order to obtain the highest possible 
degree of economy and efficiency in each case, it is usually 
necessary to treat each design separately and independently, 
especially if the bridge be one of considerable length of 
span. In doing this the designer must rely upon his knowl- 
edge of the underlying principles,and upon his own judgment 
and experience. 


PROPORTIONING THE MATERIAL. 


THE MATERIALS USED FOR SUPER- 
STRUCTURES OF BRIDGES. 


1376. The materials commonly used in the construc- 
tion of the superstructures of bridges are structural steel, 
wrought iron, and wood. 

Owing to the increasing scarcity of suitable timber and to 
the cheapness of iron and steel, together with the fact that 
metal bridges are more durable than those constructed of 
wood, the latter material is now little used for bridge 
trusses. 

In this country bridges were never constructed entirely of 
cast iron, although at one time this material was used to a 
considerable extent for compression members. On account 
of the unreliable character of this metal, however, it is no 
longer employed for the superstructure of fixed bridges, ex- 
cept for such purposes as bed-plates and small and unim- 
portant details. 


1377. A few years ago wrought iron had become the 
material used exclusively for the main parts of metal bridges; 
but, although it is still used to some extent, it is being 
largely superseded by structural steels, which are somewhat 
stronger and better materials than wrought iron, and cost 
about the same. The name structural steels is applied to 
these materials in order to distinguish them from other 
kinds of steel, such as cutlery steel and tool steel, which are 
very different. The use of structural steels is becoming 
more and more general, and the time is probably not far 
distant when wrought iron will no longer be used for 


For notice of copyright, see page immediately following the title page. 


808 PROPORTIONING® TE Beara PEs 


structural purposes. Thisis due to two reasons: First, the 
manufacture of steel is being constantly perfected and cheap- 
ened. Second, less attention is being given to the manu- 
facture of wrought iron, and on thisaccount it is not possible 
to obtain as good qualities of this material as formerly. 
Structural steels are without doubt the best of known 
materials for bridges. 


1378. When steel was first used for this purpose its 
properties were not thoroughly understood, and it was not 
as judiciously used as at present. The mistake of using 
grades of steel containing too high percentages of carbon 
was quite commonly made. Steel high in carbon possesses 
high ultimate strength and elastic hmit, but is hard and 
brittle, and not uniform; it does not weld readily, and is 
very liable to injury in forging or punching. In the earlier 
use of structural steels, the impression that all steel pos- 
sessed these unreliable properties became common; the 
brittleness of steel was also believed to be to some extent 
due to the fact that it is not fibrous. All this gave rise to 
considerable prejudice against the use of steel for structural 
purposes, and by many engineers it was considered inferior to 
wrought iron. 

But from further experience in the use of steel and more 
accurate knowledge concerning its properties, it is known 
that steel low in carbon and reasonably free from certain 
injurious elements, noticeably sulphur and phosphorus, can 
be produced that is exceedingly tough and ductile, and in 
most respects superior to wrought iron. It has also been 
satisfactorily ascertained that the fiber existing in wrought 
iron is simply a circumstance of its manufacture rather than 
any inherent property of the material itself; that it does not 
make the iron materially stronger in the direction of the 
fiber, but merely weaker in a direction across the fiber. 
Steel, having no fiber, is of nearly uniform strength in all 
directions. Knowledge of these facts has largely removed 
the objections to the use of steel, and to-day this material is 
very extensively employed. 


PROPORTIONING THE MATERIAL. 809 


Structural steels are produced by both the Bessemer and 
the Open Hearth processes. The latter process is generally 
preferred, as it is believed to give better results. 


QUALITY OF THE MATERIALS. 


1379. Wrought Iron.—Specifications for the quality 
of the wrought iron used in bridges commonly require an 
elastic limit of not less than 26,000 pounds per square inch 
for all grades, and an ultimate tensile strength varying from 
50,000 pounds per square inch, for bars of not more than 
44 square inches of sectional area, down to 48,000 pounds 
per square inch, for bars of 84 square inches of sectional 
area, or for larger bars, for shaped iron, and for plates from 
8 to 24 inches in width; and for wider plates, 46,000 pounds 
per square inch. 


1380. They also require that the specimen pieces tested 
shall before rupture elongate, in a length of 8 inches, 18 per 
cent., if from bars of not more than 44 square inches sec- 
tion; 15 per cent., if from larger bars, shaped iron, or plates 
less than 24 inches wide; 10 per cent., if from plates more 
than 24 inches and less than 36 inches wide; and8 per cent., 
if from plates more than 36 inches wide. 


1381. It is usually required that the tensile strength, 
limit of elasticity, and ductility shall be determined from a 
standard test piece of as near $ square inch sectional area as 
possible. The elongation shall be measured on an original 
length of 8 inches. 


1382. The following cold bending tests are also required: 

All iron for tension members and specimens from shaped 
iron must bend cold, without cracking, through 90° toa 
curve whose diameter is not more than twice the thickness of 
the piece. Samples from plate iron must bend cold, without 
cracking, through 90° to a curve whose diameter is not more 
than three times the thickness of the piece. Rivet iron must 
bend cold through 180° to a curve whose diameter is equal 
to the thickness of the rod tested, without sign of fracture 


810 PROPORTIONING THE MATERIAL. 


on the convex side. When nicked and bent cold, all iron 
must show a fracture mostly fibrous. 


1383. Alliron must be tough, ductile, fibrous, and of 
uniform quality. Finished bars must be thoroughly welded 
during rolling, and must be straight, smooth, and free from 
injurious seams, blisters, buckles, cracks, or imperfect edges. 


1384. Although the conditions of some specifications 
are rather more rigid, the above conditions represent a good 
quality of iron and contain no excessive requirements. It 
will be noticed that the elastig limit specified is slightly more 
than one-half the ultimate strength. This is commonly 
found to be the case for wrought iron. 


1385. In some specifications the ultimate tensile 
strength per square inch required for bar iron is written 


7,000 x area of original bar 
circumference of original bar 





52,000 — (all in inches). 


1386. The modulus, or coefficient, of elasticity of a 
good quality of double refined bar iron, as determined from 
tests made on finished eye-bars, is from 25,000,000 to 
27,000,000 pounds per square inch. It often falls much below 
these amounts, and often runs as high as 32,000,000; it is 
usually taken at 27,000,000. 


1387. Steel.—As commonly manufactured, there are 
three grades of structural steel, namely, soft steel, called 
also mild steel; medium steel, and high steel, called 
also hard steel. The following requirements are from the 
‘Specifications for Constructional Steel,” published by the 
Carnegie Steel Company, Limited. They plainly indicate 
the quality of each grade of steel ascommonly specified, and 
the properties specified for each grade may be considered as 
fairly representative of that grade: 


1388. ‘Soft Steel.—Specimens from finished material 
for tests shall have an ultimate strength of from 54,000 to 
62,000 pounds per square inch; an elastic limit of one-half 
the ultimate strength; a minimum elongation of 26 per cent. 


PROPORTIONING THE MATERIAL. 811 


in 8 inches, and a minimum reduction of area at fracture of 
50 per cent. This grade of steel to bend cold 180° flat on 
itself, without sign of fracture on the outside of the bent 
portion. 


1389. ‘‘ Medium Steel.—Specimens from finished ma- 
terial for tests shall have an ultimate strength of from 
60,000 to 68,000 pounds per square inch; an elastic limit of 
one-half the ultimate strength; a minimum elongation of 20 
per cent. in 8 inches, anda minimum reduction of area at 
fracture of 40 per cent. This grade of steel to bend cold 180° 
toa diameter equal to the thickness of the -piece tested, 
without crack or flaw on the outside of the bent portion. 


1390. ‘‘ High Steel.—Specimens from finished material 
for test shall have an ultimate strength of from 66,000 to 
74,000 pounds per square inch; an elastic limit of one-half 
the ultimate strength; a minimum elongation of 18 per cent. 
in 8inches; a minimum reduction of area at fracture of 35 
per cent. This grade of steel to bend cold 180° to a diameter 
equal to three times the thickness of the test piece, without 
crack or flaw on the outside of the bent portion.” 


1391. It will be noticed that no definite line of dis- 
tinction exists between the three grades, but that the dif- 
ferent grades blend into each other. Many specifications 
now allow a variation of 10,000 pounds per square inch in the 
ultimate strength of each grade. 


1392. It will also be noticed that for each grade of steel 
the percentage of elongation specified is practically one-half 
the specified percentage of reduction of area at fracture, and 
that the elastic limit specified is one-half the ultimate 
strength. This requirement for the elastic limit is easily 
fulfilled. Recent investigations have shown that structural 
steel having an elastic limit considerably greater than one- 
half its ultimate strength can readily be obtained. 


1393. The modulus, or coefficient, of elasticity of 
structural steel does not differ greatly from that of wrought 


I. LI.—18 


812 PROPORTIONING THE MATERIAL. 


iron; 29,000,000 pounds per square inch is probably a fair 
average value of this modulus for both soft and medium steel, 
though it is sometimes taken at 28,000,000 pounds per square 
inch. 


1394. On account of its extreme toughness and ductil- 
ity, soft steel is especially suitable for rivets, and is largely 
used for this purpose, although it is also very suitable for 
the riveted members of bridges for which it is now much 
used. 

Medium steel is the material now most commonly used in 
the construction of the main members of bridges. 

High steel is somewhat brittle, and is not very extensively 
used in bridge construction. 

Intermediate and extreme grades of steel are sometimes 
specified, as medium soft, medium hard, very soft, 
or very hard. 


THE USE OF WROUGHT IRON. 


FACTORS OF SAFETY AND UNIT STRESSES. 


1395. The nature and use of the factor of safety 
have been explained in Arts. 1214 to 1216. At one time 
it was not an uncommon practice to construct bridges with 
certain factors of safety, based upon the ultimate strength 
of the material; it was customary to use a factor of safety 
of 4 for highway bridges and 5 for railroad bridges. This 
practice is still followed to a limited extent, but the more 
modern and now quite general practice is to use certain al- 
lowed stresses, called working stresses or unit stresses, 
whose values vary according to circumstances. The unit 
stresses allowed for members which receive their maximum 
stresses often or suddenly, such as web members, and 
especially counters, are less than those allowed for members 
which receive their maximum stresses seldom or gradually, 
such as chords. 


PROPORTIONING THE MATERIAL. 813 


SPECIFICATIONS AND HAND-BOOKS. 


1396. In designing a bridge, the values given to the 
unit stresses are usually in accordance with certain specifi- 
cations which are accepted as representing reliable engin- 
eering practice. Several such specifications for highway 
bridges have been published by prominent American bridge 
engineers, notably G. Bouscaren, Theodore Cooper, Edwin 
Thacher, and J. A. L. Waddell. 

The bridge specifications most widely known, and which 
have obtained most popular recognition in this country, are 
those of Mr. Theodore Cooper, a prominent bridge engineer 
of New York City. These specifications may be said to have 
become a standard for American bridge practice. 


1397. The stresses for the various members of the 
bridge shown in detail in Mechanical Drawing Plates, 
Titles: Highway Bridge: Details I, II, III, I1V, and High- 
way Bridge: General Drawing, were obtained in Arts. 
1292 and following, and are shown written along the sev- 
eral members upon the stress sheet in Fig. 283. 

The student should, for his own convenience, make a copy 
of this stress sheet upon a sheet of paper, cap size, desig- 
nating the joints by the system of notation shown in Fig. 76 
of Mechanical Drawing. This need not be a neat copy, but 
simply a working copy, and is as well made in pencil. 

The material for this bridge will now be proportioned of 
wrought iron, according to Cooper’s ‘* General Specifications 
for Highway Bridges,” the necessary portions of which will 
be quoted in Art. 1399. 


Note.—As a copy of these specifications may be obtained for 
twenty-five cents, the student will find it to his advantage to provide 
himself with one. 

In bridge designing, one of the valuable hand-books of 
structural shapes published by several of the large iron and 
steel manufacturing companies will be found of material 
assistance. Sucha book gives the sizes, weights, sectional 
areas, and various properties of the structural shapes manu- 
factured by the company by which it is published, besides 


814 PROPORTIONING THE MATERIAL. 


convenient tables and other valuable information. In prac- 
tice, a structural hand-book is found indispensable. These 
hand-books may be obtained from the various iron and steel 
manufacturers at a small cost. 


UNIT STRESSES ALLOWED FOR TENSION 
MEMBERS. 


1398. The stresses are found in the various members 
of a bridge simply for the purpose of ascertaining the amount 
of strength required for each member, which is given such 
size and form as to best resist its stress. 

The material for tension members is more easily propor- 
tioned than for those which bear compressive stress; there- 
fore, in the example chosen, the tension members will be first 
considered. 


1399. The tensile stresses for wrought tron, in pounds 
per square inch of sectional area, allowed by Cooper’s Gen- 
eral Specifications for Highway bridges, are as follows: 

Pounds per 
Square Inch. 


(z)'-*2OnJateral: bractnee te pie ee 15,000 
(2) ‘On solid rolled beams, used as cross floor 
béams and stringers s:7 ot sleds eee eae ee ee 12,000 
(c) ‘‘On bottom flange of riveted cross-girders, net 
SECHION. (4 us los she aetna ale eet ere ae eee 12,000 
(Zz) ‘‘On bottom flange of riveted floor stringers, 
inet iSectiOn sai es cancete ee et tee eee ee 12,000 


(c) ‘fOn floor beam hangers, and other similar 
members liable to sudden loading (bar iron 
WiLD:fOreed CNS aig tws ae tn, eee teem 9,000 

(7) ‘*On floor beam hangers, and other similar 
members liable to sudden loading (plates or 


sha pes) Set SEClion i cer Mae see. open ene eee 7,000 
For For 
Live Loads. Dead Loads. 


(g) ‘‘Bottom chords, main diag- 
onals, counters, and long verti- 
cals’(forvetleye-bars)i 4% sas 10,000 20,000 


PROPORTIONING THE MATERIAL. 815 


For For 
Live Loads. Dead Loads. 
(Z) ‘‘Bottom chords and flanges, 
main diagonals, counters and 
long verticals (plates or shapes), 
PeieseourOunen. Sarssei pies nee 8 9,250 18,500” 


The following clauses from the specifications also have 
direct reference to the tension members. As is not uncom- 
mon, the word s¢razz is used in these specifications in the 
sense of sfress. 


(z) ‘‘ The areas obtained by dividing the live load strains 
by the live load unit strains will be added to the areas ob- 
tained by dividing the dead load strains by the dead load 
unit strains, to determine the required sectional area of any 
member.” 

(7) ‘Single angles subject to direct tension must be con- 
nected by both legs, or the section of one leg only will be 
considered as effective.” 


(k) Net Section.—‘‘In members subject to tensile strains, 
full allowance shall be made for reduction of section by 
rivet holes, screw threads, etc. 

‘*In deducting the rivet holes to obtain net sections in 
tension members, the diameter of the rivet hole will be 
assumed as } inch larger than the undriven rivets.” 


(7) Effect of Wind on Chords and End FPosts.—‘‘'The 
strains in the chords and end posts from the assumed wind 
forces need not be considered, except as follows: 

‘‘ist. When the wind strains per square inch on any 
member exceed one-quarter of the maximum strains per 
square inch due to the dead and live loads upon the same 
member. The section shall then be increased until the total 
strain per square inch shall not exceed by more than one- 
quarter the maximum fixed for dead and live loads only. 

‘¢2d. When the wind strain alone, or in combination with 
a possible temperature strain, can neutralize or reverse the 
tension in any part of the lower chord, from dead load 
only.” 


816 PROPORTIONING THE MATERIAL. 


(7) Lateral Rods.—‘‘In no case shall any lateral or 
diagonal rod have a less area than ? of a square inch.” 

Each of the above items, quoted from the specifications, 
is here designated by a letter for convenience of reference. 
It will be noticed that in items (a) to (/), inclusive, the unit 
stresses are for the combined live and dead load stresses, 
while in items (g) and (/) the stresses per square inch 
allowed for the dead load are just double those allowed for 
the live load. As the trusses for the example are pin-con- 
nected, the tension members will be of bar iron. The 
_ tension members of this structure will be proportioned by 

items (@), (c), (¢), and (¢). 


1400. If F is the total live load stress in pounds; 
P,is the total dead load stress in pounds; 
S, is the live load unit stress in pounds per 
square inch; 
S,is the dead load unit stress in pounds per 
square inch, and 
A is the total area of the cross-section in 
square inches; 
then, item (7) above may be concisely expressed by the 
formula | 


ene eagle 
A= (109.) 


Since, according to items (g) and (Z), the allowed dead 
load unit stress is double the allowed live load unit stress, 
we have S, =4S,, and formula 109 may be written 

MeN dee bade terme ie) 
Aas TiS oe Te (1092.) 

For clearness, the operations indicated by formula 109 
will here be followed. The operations indicated by formula 
1092 are, however, slightly shorter, and the student may 
employ them if he chooses. 


1401. Members of a pin-connected bridge, which are 
designed to resist tensile stresses only, are commonly made 
of flat, square, or round bars, and are usually placed in 


PROPORTIONING THE MATERIAL. 817 


pairs. Main tie bars and lower chord bars are usually flat 
bars in pairs; hip vertical bars are usually flat or square 
bars, but are sometimes round bars. In order that they 
may be easily fitted with turnbuckles, counters are usually 
made of square or round bars (preferably square), and are 
in pairs or single, while lateral rods are usually single round 
rods. 

In trusses having riveted connections, the tension mem- 
bers, as well‘as the compression members, are formed of 
plates or shape iron, or of the two combined. 


PROPORTIONING THE MATERIAL FOR TEN- 
SION MEMBERS. 


1402. According to item (z) of Art. 1399, the sec- 
tional area for the main tie, required by item () (see Fig. 
283), 1S an - oD = 3.24 sq. in. The section is made 
up of two bars 2” x 48”= 3.25 sq. in. As the material 
composing the required section is determined for each 
member, the student should note it upon his copy of the 
stress sheet; it should be marked along the member in 
the vzght half of the diagram of the truss. According 
to the same items of the Specifications, the sectional area 
16,200 | 4,600 
10,000 20,000 
sq. in. It is made up of two bars, each 1 inch square, 
making a total area of 2 sq. in. 





required for the hip vertical 40 is Salen 








1403. The sectional area required for the counter Cc’ 

13,750 
is —”—— 

10,000 
members in the center panel should each be made up of two 
bars, rather than one bar. As item (7) specifies that no 
diagonal rod shall have a less area than # square inch, 
which is practically to the effect that no diagonal rod shall 
pewlessmithaned inch ¢squatre A=" 706° sq... inv)/for™ 2) ‘inch 
round (=.785 sq. in.), the section of the counter Cc’ is 


= 1.38 sq. in. It is desirable that the diagonal 


818 PROPORTIONING THE MATERIAL. 


made up of two bars ¢ inch square=1.53 sq. in. The 
sectional area required by the live and dead load stresses in 
32,400 , 138,900 _ 


the panel ad or dc of the lower chord is 10,000 + 20,000 = 





3.94 sq. in. 


1404. In highway bridges the lower chords are often 
proportioned with reference to the live and dead load 
stresses only; if this were done in the present case, the 
section could be made up of two bars 24" x 413" = 4.06 sq. in. 
Likewise, for the center panel cc’ of the lower chord, the 
sectional area required by the live and dead load stresses is 
48,600 | 20,800 
10,000 * 20,000 
other stresses, the section could be made up of two bars 
A" 3) — §8sq) in= Bat ithewetlect-got ptinewwindestie-ce> 
upon the chords and posts should always be considered, 
especially in the case of a short and light structure. In 
order to comply with the requirements of item (/), it will 
be found necessary to considerably modify the section of 
the panels @6 and dc of the lower chord. But this will 
be taken up further along, after the design of the compres- 
sion members has been considered. 





= 5.90 sq: in. Without reference to any 


1405. The sectional area required for the diagonal rod in 
14,900 

15,000 
.99 sq. in. The section is made up by a round rod 14" in 
diameter = (14)’ X .7854 = .99 sq. in. The area of section 
for the diagonal in the second panel of the lower lateral 
8, 200 
15,000 
In compliance with item (7z), a round rod 1” in diameter = 
#9 sq. in, is,,used ‘for this mémpbers =/The area of seetion 
for the diagonal rod in the middle panel of the lower lateral 
2, 200 
15,000 
A round rod 1” in diameter is used for this member also. 
For the diagonal rod in the end panel of the upper lateral 


the end panel of the lower lateral system, item (a), is 


system, as required by the stress, is =O. so alias 





system, as required by the stress, is ==. bo 5c Salis 


PROPORTIONING THE MATERIAL. 819 


3,700 
15,000 ~~ 
sq. in. No stress was obtained for either diagonal in the 
center panel ‘of the upper lateral system. In compliance 
with item 7, each diagonal rod in the upper lateral system 
will be a round rod 1” in diameter. 


system, the section required by the stress is 25 


Nore.—Having obtained the sectional area required for a tension 
member, the dimensions of the bars giving the required area are 
quickly determined from a table of areas; such tables are given in 
structural hand-books. 


1406. It will be noticed that, in proportioning the 
material for the tension members, the amount of stress and 
the allowed unit stress are the only quantities considered. 
Bars for tension members should be of sizes commonly rolled 
and suitable for the practical requirements of the shop work; 
otherwise (with one exception, which will be _ hereafter 
noticed), the form of a tension member is unimportant. 


COMPRESSION MEMBERS. RADII OF GYRA- 
TION. 


1407. The form of a member which resists compres- 
Sive stress bears a very important relation to its strength. 
Failure of a strut or column is not usually the result of 
direct crushing, but of bending or buckling. The capacity 
of a column to resist compression depends upon its length 
and form, as well as upon the area of its section. Various 
forms used for compression members are shown in Fig. 303. 
Of these,-forms 4, 4, C, DY, and = are used for top chords 
and end posts; forms /, G, 7, 7, X, and Z are used for inter- 
mediate posts; although forms / and // are also sometimes 
used for top chords and end posts; forms J7, V, O, and P 
are sometimes used for lateral struts. Forms G and /are © 
seldom used on account of the difficulty of riveting; as one 
head of each rivet is within the assembled piece, it is not 
easily accessible for machine riveting, Form £ is used for 
very heavy chord and end post sections. Forms A, s, C, D, 
and & are very economical. 


820 PROPORTIONING THE MATERIAL. 


1408. In Arts. 1240, and following, the nature and 
derivation of the moment of inertia and the radius of 
gyration were explained. In the accepted formulas for 








FIG. 303. 


determining the required area for a strut of given external 
dimensions, the least radius of gyration of the section is the 
only variable quantity, when the length of the strut and the 


PROPORTIONING THE MATERIAL. 821 


character of its end connections (i. e., whether flat-ended 
or pin-ended) are constant. 

The radii of gyration of the various structural shapes 
commonly rolled may be found in any of the manufacturers’ 
hand-books previously mentioned, and, although the bridge 
designer is constantly making use of the radius of gyration, 
he seldom finds it necessary to compute it. The exact 
formulas for determining the radii of gyration of the 
sections shown in Fig. 303 are often of a complicated char- 
acter. The following are approximate formulas, which 
may be used where great accuracy is not required, and 
also for finding trial values; 7 is the least radius of gyra- 
tion, and W the depth of the section, as shown in the 
figure. 


For torms'A 74, C.D and £, 


eS 
r=—W. (110.) 


For forms /, G, H/, and /, 
ne - W. (1111.) 


For form K, 


" 5 
Ay: W. (11 2.) 
For form ZL, 


24. 


_ #= Wz 
Toma ae WV. (113.) 


For form J/ (equal legs), 


Sle. 


Yr 


For form JV (equal legs), 


pa - W. (118.) 


822 PROPORTIONING THE MATERIAL. 


For form O (longer legs back to back), 
1 


32 
Tn ana CL) 
For form P, 
? =e terion abe bets 


These formulas are very convenient to use, and obviate 
the constant reference to structural hand-books. Although 
in reality they are only approximate formulas, yet the val- 
ues for the radius of gyration given by most of them are 
believed to be sufficiently close to the correct values for 
many practical purposes. The results obtained by formulas 
110, 111, 112, 114, and 115 are quite reasonably 
accurate; those given by 113, 116, and 117 are some- 
what less accurate, while results obtained by 118 are but 
liberal approximations. On account of their convenience, 
some engineers use values for the radius of gyration obtained 
by such formulas in preference to the exact values. It is, 
however, better to take the correct values given in the 
hand-books. 


FORMULAS FOR COMPRESSION. 

1409. Formula 76, of Art. 1256, is 
Sn vt 
AlN 
1+< 7] 

af ( gl 
in which Wis the load upon the column, 5S, is the ultimate 
strength of the material in pounds per square inch, A is the 
sectional area of the column in square inches, / is a factor of 
safety, 7 is the length of the column in inches, / is the 


least moment of inertia of the cross-section, and g is a 
constant. 


Wi 








PROPORTIONING THE MATERIAL. 823 


As/=A/7?’ (Art. 1241) this formula may be written, 
ayo Aer | 


ee) 
1 Se) me, 1 2 
fi+mm) s0+s 
Omitting the factor safety f and dividing by the area A, 


the formula for the wltzmate strength per square inch of 4 
column becomes 


ie = 











= 1 (119.) 





which corresponds to the form in which this formula for 
columns is commonly written. In this form it is known as 
Rankine’s modification of Gordon’s formula, or 
simply as Rankine’s formula. In Bridge Engineering 
the following forms of Rankine’s formula are generally 











used: 
(1 20.) (121.) (1:22,) 
For two For pin and For two 
square bearings : square bearings : pin bearings. 
40,000 40,000 40,000 
7? Pas Pek, 
1 + 1+ 1 + 


36,000 7° 24,000 7” 18,000 7? 


in which 7 is the length of the column and 7 is the least 
radius of gyration, both in inches. 

These formulas have been extensively used for the ulti- 
mate strength of wrought-iron columns or struts, the results 
given being usually divided by a factor of safety of either 4 
or 5 for a unit stress or safe working stress per square inch. 
They are of the kind known as curve formulas, because, 
as they contain the squares of / and 7, if the results are 
plotted for various consecutive values of those quantities, a 
curve will be obtained. Of recent years, however, some 
simpler formulas, known as straight-line formulas, 
have come into quite general use. They are so called 
because, as they contain only the first powers of /and7, 


824 PROPORTIONING THE MATERIAL. 


the results of any one formula, if plotted, will form a 
straight line. 


1410. For wrought tron the compresstve stresses per 
square inch of section, allowed by Cooper’s General Specifica- 
tions for Highway Bridges, are gtven by the following 
straight-line formulas : 

(x) Chord Segments. 


For live load strains: 


P= 10,000 — 405, (123.) 


For dead load strains: 


P= 20,000 — 80-. (124.) 


(0) All Posts. 


For live load strains: 


P=8,750 — 505, (125.) 


For dead load strains: 
Py 500 2— 1005, (1 26.) 
For wind strains: 


P= 13,000 — 5, (127.) 


(p) Lateral Struts. 


For assumed initial strain: 


P= 11,000 — 604, (128.) 


In all of which P is the allowed compression per square 
inch of cross-section, / is the length of the compression 
member in inches, and 7 is the least radius of gyration in 
inches. As before noticed, the word s¢razz is used in the 
sense of stress. 


PROPORTIONING THE MATERIAL. 825 


1411. In using compression formulas, and in all com- 
putations relating to the proportioning of the material for 
the members of a bridge, the length of any member taken 
is always its theoretical length, 1. e., its length center to 
center of connections. The value of / is given to the nearest 
inch. 


1412. The following clauses of the Specifications also 
refer to the compression members: 


(7) ‘‘ No compression member, however, proportioned by 
the above formula, shall have a length exceeding 45 times 
its least width. For ratios greater than 45 the constants in 
the above formula will be reduced proportionately.” 


(7) ‘‘The lateral struts shall be proportioned by the 
above formula to resist only the resultant due toan assumed 
initial strain of 10,000 pounds per square inch upon all rods 
attaching to them, assumed to be produced by adjusting the 
bridge or towers.”’ 


(s) ‘‘ Members subjected to alternate strains of tension and 
compression shall be proportioned to resist each kind of 
strain. Both of the strains shall, however, be considered as 
increased by an amount equal to ,§, of the least of the two 
strains, for determining the sectional areas by the above 
allowed unit strains.”’ 


(¢) ‘* The unsupported width of a plate subjected to com- 
pression shall not exceed thirty times its thickness, except 
cover plates of top chords and end posts, which will be 
limited to forty times their thickness.” 


(7) ‘* No iron shall be used less than 4 inch thick, except 
for lining or filling vacant spaces.” 


(v) ‘‘ ln compresston chord sections, the material must 
mostly be concentrated at the sides, in the angles, and verti- 
cal webs. Not more than one plate, and this not exceeding 
8 inch fn thickness, shall be used as a cover plate, except 
when necessary to resist bending strains.” 


826 PROPORTIONING THE MATERIAL. 


DIMENSIONS OF COMPRESSION MEMBERS. 


1413. By reference to the formulas given in the pre. 
ceding articles, it will in each case be noticed that the greater 
the radius of gyration of the section the greater will be the 
unit stress, and hence the less will be the area required to 
resist the given stress. In determining the dimensions of a 
compression member by any such formulas, therefore, the 
natural course would be to select a size and form of section 
giving the radius of gyration as large as possible, which 
would also require the width and depth of the member to be 
as great as possible. If this idea were carried to extremes 
it would result in large members of very thin metal, and 
there is evidently a limit beyond which the metal would be 














too thin to be of value asa strut. To obviate this it is the 
practice to limit the ratio between the minimum thickness of 
the material and the dimensions of the piece. Thus, item 
(¢), Art. 1412, limits the ratio between the thickness and 
width of any plate in a member subjected to compression. 
In accordance with this specification, the thickness of the 
side plates in forms /7 and JB, Fig. 304, must not be less 
than one-thirtieth the distance between the two lines of 
rivets connecting them to the angles, while in form B 
of that figure the thickness of the cover plate must not be 
less than one-fortieth the distance between the two .lines of 
rivets connecting it to the angles. 


PROPORTIONING THE MATERIAL. 827 


1414. In order that the radius of gyration obtained 
according to the formula given in Art. 1408, for either 
section shown in Fig. 304 (i. e., the radius of gyration about 
the axis x x), shall be the /east radius of gyration of the 
section; the clear distance between the side plates (or 
channels, if channels are used) must not be less than that 
given by the following formulas. The formulas apply also 
to those similar forms of sections shown at A and F, Fig. 
303, in which channels are used. If W represents the width 
of the member, as shown in Figs. 303 and 304, and c repre- 
sents the clear distance between side plates or backs of 
channels, then, 


For post sections, forms / and //, Fig. 303: 


sa W,  (129.) 


For chord sections, forms A, 2, C, and D: 
7 e 
c= W. (130.) 


For a section of the form shown at L, Fig. 303, the 
radius of gyration given by formula 113, Art. 1408, 
will be the least radius of gyration of the section when the 
two pairs of angles which are connected by the lattice bars 
are separated by a reasonable distance. This distance varies 
from zero in angles having both legs of nearly equal length 
(as 3” K 24”) to about 1?” in angles having the longer leg 
double the length of the shorter leg (as 7” x 34”). Prac- 
tical considerations generally require them to be separated 
more than this. Each pair of angles is usually separated $” 
by the lattice bars. Hence, for W add 4" to the dimen- 
sion given by the two angles. 

For a section of the form QO, Fig. 303, formulas 116 
and 117 must both be applied; the smaller value of 7 
given by these formulas must be used. 

For form /, the dimension ’ must be large enough so 
that the radius of gyration obtained (in terms of IW) by 
formula 118 will be the /eas¢t radius of gyration of the 


T. II.—1} 


828 PROPORTIONING THE MATERIAL. 


section. It is impossible to give a general rule for the 
comparative dimensions necessary to satisfy this condition; 
but the radius of gyration given by formula 118 will 
usually be the least radius of gyration of the section when 
the value of V is equal to or greater than that given by the 
formula 
8 
Yi 10 W. (131.) 

In order to be on the safe side, the value of V should 
always be taken somewhat greater than given by the above 
formula. 

Forms //, O, and P are not very satisfactory forms of 
sections to use for compression members, and should not be 
used except for lateral struts, and not for this purpose when 
better forms can be as expediently used. It is generally 
much more satisfactory and economical to use symmetrical 
sections, 1. e., those in which the centers of gravity are at 
the centers of the sections. 


THE WEIGHT OF WROUGHT IRON. 


1415. Before proceeding further it will be well to 
notice how the weight of a piece of wrought iron may be 
estimated. By reference to Table 19, Art. 1184, it will 
be found that the average weight per cubic foot of wrought 
iron is 480 pounds. For rolled sections of large dimensions 
the average weight per cubic foot is slightly less than this 
amount, but 480 pounds per cubic foot is the weight 
invariably used in estimating wrought iron for bridge pur- 
poses. A bar of iron 1 foot long and 1 inch square weighs, 

480 


therefore, “7 = 34 Ib. = a Ib.- If the bar is one yardilane 


: ; : 10 ; 
its weight is 3 x > or just 10 pounds. 


Therefore, given the sectional area of a wrought-iron bar 
of any form, its weight per foot can readily be found by 
the following formula, in which A is the sectional area of 


Bi cst ine ag ot 


PROPORTIONING THE MATERIAL. 829 


the bar in square inches, and w is its weight in pounds per 
foot of length: 


ee aA. (132.) 


If w, the weight per lineal foot of a wrought iron bar of 
any form, is known, its sectional area may be found by the 
formula 

A= Re w. (133) 

1416. Wrought-iron structural shapes are rolled in 
various sizes, and each size may have any weight between 
certain maximum and minimum limits, according to the 
practical limits for rolling and the allowed minimum thick- 
ness of the metal. The variation in weight for each size is, 
for most shapes, effected by simply changing the distance 
between the rolls. 

In specifying any structural shape other than a plate, or 
a round, square, or flat bar, for which the exact dimensions 
can be readily stated, it is necessary to specify both the size 
and the weight. If the weight of a shape is not stated, the 
lightest weight rolled of the specified size is always under- 
stood. For some shapes the thickness of metal is some- 
times specified instead of the weight, though not commonly. 
Thus, a 4” x 3” angle bar having 2” thickness of metal is 
usually specified as a 4" 3” L@ 8.41b., but it may be speci- 
fied as a 4” x 3” x 2” L. The weight and the thickness of 
metal are never doth specified, as the one determines the 
other. 


1417. The maximum and minimum weights of the 
various sizes of wrought-iron channels, as commonly rolled, 
are given in the following table. All mills, however, do not 
roll channels as light as the minimum weights here given, 
nor do the maximum weights here given correspond to the 
maximum weights as rolled by all mills. The weights in 
the table, however, represent closely the least and greatest 
weight of each size as rolled by any mill. Each size can 
usually be rolled of any weight between the limits given: 


830 PROPORTIONING THE MATERIAL. 


TABLE 30. 


MAXIMUM AND MINIMUM WEIGHTS OF WROUGHT 
IRON CHANNELS. 














Size of Channel Minimum Weight, Maximum Weight, 
in Inches. Pounds per Foot. | Pounds per Foot. 
5) 5.0 6.0 
+ 0.0 10.5 
3) 5.7 14.0 
6 rao 19.4 c 
7 8.9 24.3 
8 10.0 28.0 
9 122 30.0 
10 16.0 od. 
12 20.0 93.9 
13 29.9 60.3 
15 02.0 69.0 








1418. The maximum and minimum weights of the 
most common sizes of wrought-iron angles are given in the 
following tables. Each size can be rolled of any weight 
between the limits given: 





TABLE 31. 


MAXIMUM AND MINIMUM WEIGHTS OF WROUGHT-IRON 
ANGLES WITH EQUAL LEGS. 

















Secret Minimum Minimum Maximum 
; Thickness of | Weight, Pounds} Weight, Pounds 
pe Nae Metal in Inches. per Foot. per Foot. 

NED 7 2.4 4.8 
24+ X AL he 2.6 6.0 
DEUS Od _ 3.0 8.0 
23 x 23 e 4.4 8.8 

3x3 1 4.8 11.4 
34 x 34 Jy 6.8 14.0 

4x4 te 8.0 Los0 

ox 5 2 12.0 32.8 

Ga<s0 3 14.0 38.5 








PROPOR TIONING THEsMATERIAL. 831 


TABLE 32. 


MAXIMUM AND MINIMUM WEIGHTS OF WROUGHT-IRON 
ANGLES WITH UNEQUAL LEGS. 























Minimum Minimum Maximum 
Size of Angle | Thickness of Weight, Weight, 

in Inches. Metal Pounds per Pounds per 
in Inches. Foot. Foot. 
24+ x15 75 2.2 5.4 
Se 2 * 2.6 7.1 
Due ce a's a.d 8.0 
3 X 24 1 4.4 a3 
* 34 x 2 4 4.2 8.8 
By X 2 42 4.0 6.6 
oy X 24 4 4.8 10.2 
a4 X93 +5 6.4 15.4 
te eer +5 6.8 16.8 
4 xX 34 <5 tO 18.1 
44 xX 3 ?o iG 18.1 
Biya ran 8.0 19.5 
5 xX 34 +5 8.5 22.9 
5 x4 2 10.8 23.1 
54 X 34 3 10.8 pale: 
6 x 34 3 Lise 1.3 
6 x4 3 12.0 1 
64 x 4 3 12.6 33.6 
CER 4 LGeY 31.7 
8 xX 34 {o 164 aia) 

















Nore.—As herein used, the weight of an angle corresponding to 
any specified thickness of metal will be the weight as estimated from 
the exterior dimensions of the angle. Thus, the weight per foot of a 
3" < 3" angle of }” thickness of metal is (8+ 38)xk4+x12=5 lb. As 
actually rolled, however, the weights per foot are slightly less than 
the weights as thus estimated, as will be noticed in the preceding 
tables. In estimating the thickness of an angle from the weight, the 
thickness will usually be taken at the full sixteenth of an inch nearest 
to the thickness, as estimated on the above basis. 


* Now rolled only in steel. 


832 PROPORTIONING THE MATERIAL. 


EXAMPLE.—What is the minimum area of section given by two 
6-inch channels ? 


SoLuTIoN.—By Table 30, Art. 1417, the minimum weight of a 
6-inch channel is 7} pounds. Therefore, by formula 133, Art. 1415, 
the minimum area of section given by two ‘7-inch channels is 
(Qipe cre # == 4.080.090.) guts: 

EXAMPLE.—A section of 10.2 square inches is to be made up of a 


12" « #" plate and two 8-inch channels. What is the weight per foot 
of each channel ? 


SoLuUTION.—The area given by the plate is 12” x #”=3 sq. in., and, 
therefore. the area to be given by the two channels is 10.2—3= 7.2 
sq. in. By formula 132, Art. 1415, the weight per foot of each 


channel is 7.2 « By x : =i ib: Ans. 


Bae eo 


EXAMPLES FOR PRACTICE. 


1. What is the least area of section that can be made up of two 
9-inch channels without wasting material ? Ans. %.65 sq. in. 


2. It is required to make upa section of 16 square inches of two 
10-inch channels and a 14" * 2” cover plate. What is the weight of 
each channel ? Ans. 17.92 Ib. 


3. Can a section of 7 square inches be made up of two 4-inch 
channels ? 


4. How large channels can be used in making up a section of 
6.2 square inches with two channels ? Ans. 8 in. 


5. A section is composed of two 6-inch channels weighing 8 pounds. 
per foot each, and a 10” x 4” cover plate. What is the area of the sec- 
tion ? . ANS? 1:5 8d= 105 


6. What is the minimum section given by four 3}" « 2” angles? 
Ans. 4.8 sq. in. 


7. What is the weight per foot of each of four 4” x 3” angles of 
which a section containing 8.4 square inches is composed ? 


ADS. (als 
8. A section of 4.8 square inches is made up of two 5" x 3” angles. 
What is the weight per foot of each angle ? Ans. 8 lb. 


9. A section of 21 square inches is made up of two 16” x 8" plates 
and four 3” x 3” angles. What is the weight per foot of each angle ? 
Ans. 7.5 Ib. 


PROPORTIONING THE MATERIAL. 833 


PROPORTIONING THE MATERIAL FOR THE 
COMPRESSION MEMBERS. 


1419. Chords and End Posts.—For the upper chords 
and end posts of the bridge shown in Mechanical Drawing 
Plate, Title: Highway Bridge: General Drawing, the effect- 
ive section is of the form shown at A, Fig. 303, being made 
up of two channels and a cover plate. In selecting the size 
of channel it is not always possible to choose at first trial 
the size most suited to the required section, two or more 
trials being often necessary. But after a certain amoynt of 
experience the designer is able to judge quite correctly of 
the size of channel most suitable to use. In the present 
case, 7-inch channels will first be tried for the top chord. 


1420. The width of the flange of a channel is given 

approximately by the formula 
F=.6 +22 W, (134.) 

in which / is the width of the flange and IV is the depth of 
the web of the channel, both in inches. By combining 
formula 134 with formula 130, of Art. L414, it is evident 
that when chord sections are made up of two channels and 
a cover plate, the width 7 of the cover plate or top plate in 
inches must somewhat exceed the value 


T=_W+3(.6-+.3W) = 124+128W.  (135.) 

The width of the top plate should always be slightly more 
than the width given by this formula, because the width of 
the flange of the channel is liable to vary considerably from 
the width given by formula 134A, and it is essential that the 
flange of the channel should not project beyond the edge of 
the cover plate. 


1421. With 7-inch channels, then, the width of the top 
plate must be somewhat more than 1.2 + 1.28 x 7 = 10.16 
inches. A width of 11 inches will be taken. 

The general dimensions of a section are often spoken of 
as the size of thesection. Forinstance, in the present case, 


834 PROPORTIONING THE MATERIAL. 


the section may be called a 7” & 11” section, without refer- 
ence to the weight of the channels or thickness of the cover 
plate. 

By formula 110, Art. 1408, the least radius of gyration 
of a section made up of two 7-inch channels and an 11-inch 
cover plate 1834, % %='2.3 ine 7. Ins the examplesuae 
length. of .a top-chord amémber “is 18" tt, —.210 inte 
Therefore, with 7-inch channels the live load unit stress 
allowed for this member by formula 123, Art. 1410, is 


216 


10,000, = 40 x 5. = 6, 91L010., and the dead load unit stress 





.8 
allowed by formula 124 of the same article is 20,000 — 
216 ; : 
80 X oat 13,820 lb, \The> dead load unit sstresemis smear 


rages) 

quickly obtained by simply doubling the lve load unit 

stress. ‘Thus, 6,910 « 2==13;78200lbs, fPiie-amounmegresc: 

tion required for the upper chord (see stress sheet) is, 

theretore; Tis aa Sa = 8.54 square inches. 
This*section’ can be*made up by aeplate 117 x= 2 

square inches, and two ‘-inch channels, each weighing 


RE Ds: ne 0:65: 1b pen tt. (mee. tortillas bee 
o 


BAtt. ee Ss) 


1422. The size of channels and width of cover plate 
for the end post should be the same as for the upper chord. 
The length of the end post, center to center of connections, 
is 25' 58” = 305.6" = 7.. By formula 125, Art. 1410, the 
live load unit stress that may be allowed, using -inch 
305.6 

2.8 
Ib., and the dead load unit stress is 3,290 x 2 = 6,580 Ib. 
Therefore, with 7-inch channels the amount of section 





channels for the end post, is 8,750 — 50 x ——onedu 





: 
required for the end post (see stress sheet) is a. 
19,600 -_ . ee Paes 
6,580 — 16.90 sq. in. If a 11’ x 75" (=4.81 sq. in.) cover 


plate is used, the weight per foot of each channel will be 


PhO NTNG. Le Bea MAE RTAL 835 


(16.90 — 4. 81) 

2 5 
sections for the chord and end post required by the use of 
7-inch channels, it will be well to compare the amount 
of section required by using 8-inch channels. 

By formula 135, Art. 1420, the width of cover plate 
required with 8-inch channels must exceed 1.2+1.28 x 8= 
11.44"; a 12-inch cover plate will be used. By formula 110, 
Art. 1408,. the least radius of gyration of a section com- 
posed of two 8-inch channels and a cover plate is #4 x 8 = 
3.2". The live load unit stress allowed by the specifications 
(formula 125, Art. 1410) is 8,750 — 50 x — =o 970 
ime Hewread load. unit stress. is 3,975 x 2 = 7,950. Ib. 
Therefore, with 8-inch channels, the amount of section 
45,800 . 19,600 
3,975 7,950 
The section given by a 12” xX 2” cover plate is 4.5 sq. in., 
and by using this size of plate the weight per foot required 
(13.99 — 4.5) . 10 

2 

With 8-inch channels the live load unit stress allowed for 
the upper chord (formula 123, Art. 1410) is 10,000 — 

216 

3.2 
is 7,300 x 2= 14,600 lb. Therefore, the section required 
48,600 20,800 _ 
7,300 14. 6K 
8.08 sq. in. According to item (w~), Art. 1412, the thick- 
ness of a cover plate must not be less than }+inch. The 
section given bya 12” x }” cover plate is 3 gare inches, 
and the ve per fat required for each channel ? 
es = 4 x ~ = 647 Ib. According to Table 30, Art. 
1417, the minimum weight of 8-inch channel is 10 pounds 
per foot; therefore, if this size channels are used, the upper 
chord must have a section of 3+ 10 x #3, X 2=9 sq. in.. 
which is somewhat in excess of the section required. 





20Pla pounds per toot, «With these 








required for the end post is == 13.99 sq. in 


== 15.82-1b. 





for each channel is 





40 X = 7,300 lb., and the allowed dead load unit stress 


for the upper chord (see stress sheet) is 





836 PROPORTIONING THE MATERIAL. 


The section made up by using 8-inch channels can now 
be compared with that in which 7-inch channels are used, 
in order to determine which section is the more economical. 

If 7 is the length in feet of a piece of iron of uniform cross- 
section A, then its weight is (formula 132, Art. 1415) 


a Al. For the upper chord, /=3 x 18 = 54; for the Zwe 


end posts, / = 2 x 25.47 = 50.94. With 77-inch channels 
the area (A) required for the upper chord = 8.54 sq. in. ; 
for each end post, d = 16.9 sq. in. With 8-inch channels 
the corresponding “values of, A are) 9 “and 14. sqau 
(nearly). Therefore, the weight of iron required by the 
v-inch channels = > 0:04 x 544 < 1059 Xe see 


a (8.54 x 54+ 16.9 x 50.94); and that required by the 


8-inch channels = = (9 x 54+14 x 50.94). The ratio of 


the former to the- latter is 


8.54 x 54+ 16.9 x 50.94 1,322 _ | 1, 
9 541A 50, O49 ee 0 eee 





By using 7-inch channels, therefore, 10 per cent. more of 
iron is required than by using 8-inch channels. ‘The latter 
will be used. 


1423. For the top chord the section will be made up of 
two 8-inch channels, each weighing 10 pounds per foot, and 
a 12” x 4” cover plate, giving a total area of section of 
9 square inches. For the end posts the section will be 
made up of a 12” x 3" cover plate and two 8-inch channels, 
each weighing 16 pounds per foot, giving a total sectional 
area of 4.5+ 16 xX 33, X 2=14.1 sq. in. Channels weigh- 
ing 15.82 pounds per foot would give sufficient section, but 
the 16-pound channels can usually be more readily obtained, 
and the difference between the two weights is not material. 


1424. The zutermediate posts will be made of four 
angles connected in the form shown at Z, Fig. 303. By 
reference to Fig. 3 of Mechanical Drawing Plate, Title: 


PROPORTIONING THE MATERIAL. 837 


Highway Bridge: Details I, it will be seen that the con- 
nected legs of the angles are separated } inch by the lattice 
bars. Therefore, if 34” x 2” angles are used, the width W 
of the section equals 33” + 4” + 34” = 74", and by formula 
113, Art. 1408, the least radius of gyration of the 
Se ODIs 7 le ee 7. he Jeneth of the post is 
faetter 216 22/- by sformula, 125, Art.. 1410, the 
allowed live load unit stress is 8,750 — 50 x ad a= 2.750 1b. 
the dead load unit stress is 2,750 x 2= 5,500 Ib. There- 
fore, the section required for the intermediate post is 
9,700 . 2,300 
2-750 | 5,500 

By formula 132, Art. 1415, the weight per foot of 
each one of the four angles necessary to make this section 


would be ae M a = 3.29 lb. But by reference to Table 32, 








= 0.00, 5. 101, 


of Art. 1418, it is seen that the lightest weight of 34” x 2” 
angles is 4 pounds per foot, and also that the thickness of 
metal for this weight is 4? inch, or slightly less than 4 inch. 

According to item (v7) of Art. 1412, the metal in a 
member must not be less than 4} inch thick. For } inch 


Q 1/7 


_ thickness of metal the weight per foot of a 34 2” angle, 
; 10 
as computed, is (3.5+2)x4i-x com 4.6 lb. The actual 


weight, however, is 4.4 pounds per foot. 

The sectional area given by four 34” « 2” angles weighing 
4.4 pounds to the foot is 4.4 x #3, Xk 4= 5.28 sq. in., which 
is somewhat in excess of the area required. 

By using 3” x 2” angles the radius of gyration would be 
.24 X 6.5 = 1.56 inches. The allowed live load unit stress 
216 
1.56 
unit stress would be 1,830 x 2= 3,660 lb. The sectional 
area required for this size of angle would, therefore, be 
9,700 . 2,300 
1,830 ' 3,660 
of the four 33” x 2” x i” angles. Four 3}’ xX 2” angles 





would be 8,750 — 50 x =,1,830 lb., and the dead load 





= 5.93 sq. in., which is more than the section 


838 PROPORTIONING THE MATERIAL. 


could have been used, however, with slightly better economy. 
The 34” x 2” size of angles was used on account of showing 
the connections rather more plainly. 


1425. The zntermediate lateral struts are proportioned 
according to items (/) and (7) of Arts. 1410 and 1412. 
By reference to item (7) it will be noticed that the lateral 
struts are not proportioned according to the stresses ob- 
tained for them, but are proportioned ‘‘to resist only the 








1 
Scale of forces 128000 lbs. 
4 2 
‘* 
as 
3 


FIG. 305. 


resultant due to an assumed initial strain of 10,000 pounds 
per square inch upon all rods attaching to them.” For any 
strut, the resultant due to the assumed initial strain, or 
stress, may readily be found by simply drawing a force 
polygon for the joint at either end of the strut. The con- 
struction for finding the resultant of the assumed initial 
stress upon the rods attaching to the strut C C, is shown in 
Fig. 305. In the diagram of the upper lateral system, the 
strut C C, and the rods attaching to it are shown by full 
lines, while all other portions of the diagram are represented 


PROPORTIONING THE MATERIAL. 839 


by dotted lines. Bow’s notation is used with reference 
to the strut and the attaching rods. The rods are round 
and 1 inch in diameter. (See Art. 1405.) The section 
of a round rod 1 inch in diameter is .785 sq. in., and, 
therefore, the amcunt of the initial strain assumed for each 
rod is 10,000 x .785 = 7,850 lb. This strain (stress) is 
evidently tension. 

Now, considering the forces acting upon joint C, the line 

1-2 is drawn -parallel, and to any convenient scale is-made 
equal to the action of the assumed tension in C C,= 
7,850 Ib.; 2-3 is drawn equal and parallel to the tension in 
CB, =7,850 lb. Then, as 1-2 and 2-3 are equal, 3-1 will be 
parallel to and represent the compressive stress in C C,, due 
to the initial stresses in C 4, and C C,; it scales 11,400 pounds. 
If the sectional area of C C, were less than that of C Z,, the 
line 7-2 would be shorter than the line 2-3, and a line drawn 
from 3 to 1 would not be parallel to C C,. In order that 
the closing line 3-1 may be parallel to C C,, in such a case, 
it will be necessary to introduce in the force polygon a line 
representing the difference between the longitudinal com- 
‘ponents of the stresses in CC, and C B,, which is taken by 
the chord CC’. The resultant of the initial stresses in the 
rods C, / and C, C’ simply resists the resultant of those in 
C Band C C,, the chords not being required to act. By 
drawing the force polygon 3-4-1-3 for joint C,, the same 
amount of stress, 11,400 lb., is obtained for C C, as before, 
while the positions and directions of the arrow-heads in the 
two polygons indicate that the resultant stress in C C, is 
compression. 


1426. The amount of the resultant stress in a strut can 
also be obtained by applying the following general 


Rule.—Divide the length of the strut by the length of the 
rod, and multiply the quotient by the assumed stress in the 
rod. The result will be the stress in the strut due to the in- 
atial stress in that one rod. The sum of the results thus 
obtained for all rods attaching to one end of the strut will be 
the total resultant for the strut. 


840 PROPORTIONING THE MATERIAL. 


The lengths used should be the lengths between the 
points where the center lines of the lateral struts intersect 
the center lines of the chords. 

The resultant R of the assumed stress upon each rod, as 
given by the above rule, may be expressed by the equation 


Sats 
/ ? 


Le 


AO 





(136.) 


in which S, is the assumed initial stress, 7. is the length of 
the rod on which the stress is assumed, and /, is the length 
of the strut for which the resultant is obtained. 

Thus, in the present case, the theoretical length of the 
strut CC, is 19 ft., and that of the rod CB, is 18? +19? = 
26.17 ft. The amount of initial stress assumed for the rod 
is 7,850 lb.’ Hence, the resultant stress in therstrute <c. 
due to the initial stress in the rod C B, is 7,850 X — = 
5,699 lb. The resultant due to the assumed initial stress 
in CC, is the same as found for CB,. The resultant due to 
both rods, therefore, is 5,699 + 5,699 = 11,398, or practically 
11,400 lb. All conditions for the lateral strut C’' C, are the 
same as for CC,; hence, each of the intermediate lateral 
struts is to be proportioned to resist a resultant compressive 
stress of 11,400 Ib. 


1427. The section of two 5’x 3” angles with the longer 
legs riveted together, back to back, in the form shown at O, 
Fig. 303, will first be tried. This is not a symmetrical sec- 
tion, but it is probably the best form to be used for the 
lateral struts when the lateral rods connect on top of the 
chords. For this section the dimension V will be 3 + 3 = 6in., 
and the dimension VY will be din. By applying formulas 


116 and 117, of Art. 1408, it is found that 7, = = y 


Fc PSM ee ace a TR at ghee a x D— 6 im) ol hererorces ee 


least radius of gyration of the section is 1.2 in. The length 
of the strut is 19 ft.= 228in. By formula 128, Art. 1410, 


PROPORTIONING THE MATERIAL. 841 


28 
the allowed unit stress for this strut is 11,000 — 60 x 
which gives no unit stress. It is, therefore, necessary to 
try angles of larger size. 

Two 5" x33" angles, with the longer legs back to back, 
will next be tried. For this section the dimension VW will 
equal 34+ 34=7 inches. Formulas 116 and 117, Art. 
Meera eive 7.4 2d in, and. 7, — 00 Or 6 
inches; 1.4 inches is, therefore, the least radius of gyration 
of the section. The allowed unit stress for this strut is 


11,000 — 60 x ee es = 1,230 lb. The sectional area required 








as = 9.27 square inches, making the weight per foot 
set | 
of each angle - x Pe a {5046 Ih. 


By reference to Table 32, Art. 1418, it is found that 
this weight is in excess of the minimum weights of angles of 
larger size, and it will, therefore, be more economical to use 
larger size angles. 

By using two 5’x 4” angles, with the 5-inch legs back to 
back, the dimension IJV will equal 4+ 4=8 inches, and the 
dimension V will remain as before. By applying formulas 
Meritt toe eo lf in., and, 7, = XB x 5 
1.6 in. When the radius of gyration of a section about 
each of two perpendicular axes is the same, as in the present 
case, the section is said to be a balanced section. It is 
evident that a balanced section is the most economical 
section to use for a compression member. The allowed unit 

228 





stress for this section is 11,000 — 60 x ao 2,450 lb., and 
-U 
é . 11,400 : 
the area required for the section is > 450 = 4,00. 40)... 11). 


Hence, the weight per foot required for each angle is 


ese a =".75 lb. Table 32, Art. 1418, gives 10,8 Ib. 


842 PROPORTIONING THE MATERIAL. 


as the minimum weight per foot of 5” x 4” angles, giving 
for two angles a sectional area of 10.8 X 2 X 33; = 6.48 sq. in. 
Although the sectional area given by the minimum weight 
of two angles of this size is found to be considerably in 
excess of the area required for them, it has also been found 
to be less than the area required for angles of smaller size. 
Therefore, each intermediate lateral strut will be made up 
of two 5” x 4” angles, each weighing 10.8 pounds per foot. 


1428. The Portal Bracing.—The design of the 
portal bracing is largely a matter of judgment; the investi- 
gation of the stresses which has been made will, however, 
be found a very helpful guide. In proportioning the 
material for this member the methods of engineers differ. 
The method here explained and followed will give very 
reliable results when a straight-line compression formula is 
used. It does not apply so well to curve formulas, but may 
be used without material error. Substantially the same 
results are obtained by other methods. 

The stresses at intervals of one foot along each flange of 
the portal are shown in Fig. 278, to which the student is 
referred. The stress at each point along the upper flange 
is somewhat greater than the corresponding stress in the 
horizontal portion of the lower flange. On account of the 
inclinations of the brackets the stresses as found along those 
members are greater than in the corresponding portions of 
the upper flange. But, as the horizontal portion of the 
lower flange extends to and connects with each end post, it 
probably relieves the stresses in the flanges of the brackets 
to a very considerable extent. To what extent it does so, 
it is, of course, impossible to say, but the actual conditions 
will undoubtedly be fully provided for if the upper flange be 
proportioned to resist its stresses as found, and the lower 
flange be given the same section as the upper flange. By 
reference to the figure it will be noticed that, where the 
depth of the portal is uniform, the stresses at the various 
points along the upper flange vary by a practically constant 
difference. Now, neglecting the fact that the stresses in 


PROPORTIONING THE MATERIAL. 843 


the upper flange decrease at the left of c, by reason of the 
increased depth of the portal, and assuming that the stress 
atthe left-of 2 is uniform and equal to the stress at c = 
+ 23,520 pounds, that portion of the upper flange which is in 
compression may be considered to be divided into a series 
of (seven) elementary struts of varying lengths. Designa- 
ting each elementary strut by the letter at its right extremity, 
the length of each elementary strut and the amount of stress 
borne by it are as follows: 


Strut c: Stress = + 23,520 —19,820=+ 3,700lb. Length = 3.5 ft. 
Strut d: Stress = + 19,820 — 16,180 = + 3,6901b. Length = 4.5 ft. 
Strut ¢: Stress = + 16,130 — 12,480 =+ 3,700lb. Length = 5.5 ft. 
Strut 7: Stress = + 12,480— 8,740=+ 3,6901b. Length = 6.5 ft. 
Strut g@: Stress=+ 8,740— 5,050=-+ 3,6901b. Length = 7.5 ft. 
Strut 4: Stress=-+ 5,050— 1,350=+4 3,7001lb. Length = 8.5 ft. 
Strut z: Stress=-+ 1,350 = + 1,350lb. Length = 9.5 ft. 


23,520 


The increment of the flange stress, or difference between 
the stresses at two adjacent points on the flange, is actually 
about 3,695 lb. The increment, or amount of stress borne 
by each elementary strut, as obtained above is, in each case, 
either 3,700 or 3,690 lb. This slight irregularity is due 
simply to the fact that each stress is written to the nearest 
ten pounds. 

As the amount of stress is the same upon each elementary 
strut (except strut z), therefore, in order to resist the same 
amount of total stress, the total area of section required for 
the seven elementary struts will be the same as the sectional 
area required for a single equivalent strut of the average 
length, assuming the radius of gyration to be the same. 
This will be the case when a straight-line compression 
formula is used, but it will be only approximate for a 
curve formula. The slight error due to the fact that the 
stress upon strut z is less than upon each of the other 
struts may be neglected; this small error in the length of 
the equivalent strut will be on the side of safety; that is, 
the equivalent strut will be slightly too long. 

The average length of the seven elementary struts is 


T. I1,—19 


844 PROPORTIONING THE MATERIAL. 
sca a = 6.5 ft. = 78 in, = 7 "THE struts ssupponeued. 
one direction by the lattice bars, and, therefore, its radius 
of gyration in that direction (about an axis perpendicular 
to the plane of the lattice bars) need not be considered. 
The two flanges of the portal, connected by the lattice 
bars, form a section similar to that shown at ZL, Fig. 303, 
and its least radius of gyration is found by formula 113, 
Art. 1408. Using 33” x 24” angles, with the shorter legs 
back to back, separated 4” by the lattice bars, the dimen- 
sion W will equal 3§ + 4-+ 34 = 74 in., and the least radius 


of gyration will be ae x 7 Ds=1lv8 me Hence, the allewea 





100 
unit stress is 11,000 — 60 x = = 8,400 lb., and the sectional 
area required is a =(2.80vsqiin. tin! Tabless2sercrt 


1418, the minimum weight per foot of a 34” x 24” angle 
is given at 4.8 lb. For the upper flange two of these angles 
will be used, giving a sectional area of 4.8 x 2 x i == BeOO 
sq. in. The lower flange and the flange of the bracket will 


be made the same. 


1429. It will be noticed that in proportioning the 
material for the flanges, two stresses only have been used; 
namely, the greatest stress, which, with a straight bracket, 
asin the figure, occurs at a point opposite to where the 
bracket connects to the horizontal flange, and the least 
stress, which may be considered to occur at the center. 

For appearance, the portal brackets of a bridge are 
often curved and otherwise ornamented. In case of a 
curved bracket, the greatest stress in the upper flange will 
occur vertically opposite that point where a line drawn 
through the center of the upper flange becomes tangent to 
the curve of the bracket. 


1430. Let us now determine whether the area of the 
section as obtained above is sufficient to resist the greatest 


PROPORTIONING THE MATERIAL. 845 


tensile stress in compliance with item (/£), Art. 1399. 
By reference to Mechanical Drawing Plate, Title: Highway 
Bridge: Details II, it is found that 8” rivets are used. 
Ateach point where lattice bars connect, one rivet passes 
through each angle, and, therefore, according to item (4), 
two rivet holes 2” + 4” = 2?” in diameter must be deducted 
from the section. Table 32, Art. 1418, gives.} inch as 
the thickness of metal for the minimum weight (4.8 pounds 
per foot) of 34” x 24” angles. Hence, the section to be 
deducted for the two rivet holes is ? X + XK 2=.3875 sq. 
in., and the net section remaining is 2.88 — .388 = 2.50 sq. 
ienebyeitemy (2), OL Art. 1399, the tensile “stress ; per 
square inch allowed for lateral bracing is 15,000. There- 
fore, the net section remaining after deducting the rivet 
holes will bear an amount of stress equal to 2.5 x 15,000 
= 37,500 lb., or more than the greatest tensile stress occur- 
ring in either flange of the portal. It is thus found that 
the section given by two 33” x 24” angles, each weighing 
4.8 pounds per foot, fulfils the necessary conditions for 
either compression or tension in the flange of the portal. 

It is to be observed that, in proportioning the material 
for the flanges of the portal, the condition required by 
item (s), of Art. 1412, has not been fulfilled. Any por- 
tion of either flange of the portal is subject to alternate 
stresses of tension and compression, and, therefore, accord- 
ing to item (s), each stress should be increased by an 
amount equal to ;8, of the smaller stress. This condition, 
however, may be neglected, as is often done. 


1431. The size of the lattice bars remains to be con- 
sidered. It is not customary to proportion the lattice bars 
according to the stresses; indeed, it is very seldom that 
the stresses are found for the lattice bars. Relying upon 
their judgment and experience, bridge engineers are usually 
able to decide upon proper dimensions for lattice bars 
without finding the stresses. 

In the present case, however, attention will be given to 
the stresses in proportioning the lattice bars. By the 


846 PROPORTIONING THE MATERIAL. 


method explained in connection with Fig. 280, of Art. 
1314, stress was found in a lattice bar on the assumption 
that the web stress due to the increment of the flange stress 
is borne entirely by the tensile lattice bar connecting at the 
given point on the flange. 

This assumption was made for convenience in finding the 
stress; the total amount of stress in the bars connecting at 
one point is the same, whether it be borne entirely by one 
bar or divided between the two bars, and it can always be 
correctly found in this manner, so long as both bars have 
the same inclination. In proportioning the material, how- 
ever, it is reasonable to assume that the total web stress due 
to the increment in the flange stress at any one point is re- 
sisted in equal parts by the two lattice bars connecting at 
the point, one bar being in tension and one bar in compres- 
sion. The strength of the lattice bars will be investigated 
on this assumption. ‘The increments in the flange stress, 
and hence the stresses in the lattice bars, are uniform where 
the depth of the portal is uniform. Where the depth of the 
portal increases, the stresses generally decrease, and may be 
neglected. 


1432. Where the portal is of uniform depth, the web 
stress due to the increment of the chord stress at any point 
was found to be 5,230 lb. This total stress is assumed to be 
equally divided between the two lattice bars connecting at 
the point, tension in one bar and compression in the other. 
The tension bar will first be considered; its stress is ae = 
2,620 lb. The size of the lattice bars will be taken at 
2” x £”; it is to be determined whether the sectional area 
given by this size of bar will be sufficient to resist the 
stress. 

The sectional area of a lattice bar of this size is2 x += 
.5 sq. in., while the area to be deducted for the rivet hole 
is $X4=.19 sq. in., leaving for tension a net sectional 
area of .5 — .19=.31 sq. in. By item (2); Art) 1399) 
the amount of tensile stress which can be borne by this 





PROPORTIONING THE MATERIAL. 847 


section is 15,000 x .31 = 4,650 lb., which is greater than 
the amount of tension (2,620 lb.) that it is required to 
bear. 


1433. The compression bar will now be considered; its 
stress is 2,620 lb., the same as the tension bar. By refer- 
ence to Table of Moments of Inertia, it is found that+the 
value of the moment of inertia / of a rectangular section is 
given by the formula 

b a* 
j= qt (137.) 
in which @ is the width of the section, or dimension parallel 
to the axis, and dis the depth, or dimension perpendicular 
to the axis. By reference, also, to formula 72, of Art. 
1241, it is found that for any section the moment of in- 
ertia /= A 7’, in which A is the area of the section and 7 is 
the radius of gyration. By equating these two values of / 
for a rectangular section, we get 


ba? 
Ar =AagCe 


(138.) 

But the area Ad = 0d; by dividing both terms of equation 
138 by the area, we have for the square of the radius of 
gyration 


no 


on se (139.) 





~ 


e 


By extracting the square root, 


a ; 
r= 3-764 — -289 a. (140.) 

In applying this formula, @ must always be the dimension 
perpendicular to the axis. If the strut is unsupported in 
either direction, as in the present case, the /eas¢ radius of 
gyration of the section must be obtained; in order to obtain 
the /east radius of gyration of a rectangular section, the 
least dimension must be taken for the value of d. 

In the present case, for the least radius of gyration, 


848 PROPORTIONING THE MATERTAL, 


a= 4} and “7 = 289. % 2.25 = "0723 ine pec hecomt yr. 1a 
lattice bar is supported by its connection with each tension 
lattice bar, and, as each compression bar is riveted at its 
supports, each separate strut length of the bar partakes 
somewhat of the nature of a strut having fixed ends; there- 
fore, the clear distance between its connections may be 
taken as the column length of the compression bar. This dis- 
tance is about 6.36 inches. By formula 128, otf Art. 1410, 





the allowed ‘unit stress is 11,000 — 60 x ae = dat ete bes 
. 2,620 
and the sectional area required for the bar is BOQ = 46 


Sq: in., ora little: less than the aréa-olja 2 <n @Date Eats 
thus found that 2” x 4+” lattice bars will fulfil the conditions 
for both tension and compression. 


1434. The Shoe Strut.—A strut should always be 
placed between the two shoes at the expansion end of a 
bridge; in important structures a strut is often placed 
between the shoes at the anchored end also. It is impossi- 
ble to determine definitely the maximum amount of stress 
that may come upon ashoestrut. Under certain conditions 
it could equal the total amount of wind pressure against the 
windward shoe, but the presence of such conditions is so ex- 
ceedingly improbable as to be practically impossible. It is 
a not uncommon practice to design the shoe strut to resist 
one-half the total wind pressure against the windward shoe, 
and this is a reasonable practice. 

As, however, the shoe strut is a lateral strut, in compli- 
ance with item (7), of Art. 141 2, it must be proportioned to 
resist the resultant due to an assumed initial stress of 10,000 
pounds per square inch upon the lateral rod attaching at 
either end. The size of each diagonal rod in the end panels 
of the lower lateral system is 14 inch round, having a sec- 
tional area of practically one square inch. (Art. 1405.) 
Therefore, the amount of initial stress assumed upon each 
rod is 10,000 pounds. In Art. 1426, the theoretical length 
of the diagonal lateral rods was found to be 26.17 feet, and, 


PROPORTIONING THE MATERIAL. 849 


according to the rule there given, the resultant stress in the 
shoe strut is 10,000 x sats 7,260 lb. In order to illus- 
trate the application of the compression formulas to as 
large a variety of sections as possible, a section of the form 
shown at P, Fig. 303, will be used. The section given 
by two 33” x 24” angles having the shorter legs riveted 
together, with a 6” x +” plate between them, will be tried. 
For this section the dimension IV is equal to 34+ 34}=7 
in., and the dimension / equals 6 in. According to formula 
131, Art. 1414, the radius of gyration given by for- 
mula 118, Art. 1408, will be the least radius of gyration 


; bf 8 
of the section when the dimension lV is not less than {0 W. 


Reet ty Gs 
Ingthe. present: cases = a airy 
radius of gyration of the section ist x 7 = 1.4 inches, as 
given by formula 118. As the actual length of the shoe 
strut, as given in the detail drawings, is not known when 
the material is proportioned, the length to be used in 
proportioning the material will be taken equal to the clear 
distance between the end posts. In the present case, this 
distance is 18 ft. = 216 in., which is the value that will be 
given to / in the eae formula. By formula 128, 

216 
i a 
7,260 
1,740 

sq. in. By Table 32, Art. 1418, the minimum weight per 
foot of a 34” x 24” angle is 4.8 lb.; hence, the total sectional 
area Eee by two 34” < 24” angles and a 6” x }’ plate is 
48x 3 x2+6x+4=4.388 sq. in. This sectional area, 
eHpuich ee Stiri in excess of the area required, will be 
used. The connections for this strut are eccentric, 1. e., 
not symmetrical with reference to the center of gravity of 
the strut. As this eccentricity tends to weaken the strut, 
some excess of section is very desirable. A symmetrical 
strut would have been better for the purpose. 


W; therefore, the least 








1,740 lb.; hence, the sectional area required is 5 aoa 


850 PROPORTIONING THE MATERIAL. 


THE EFFECT OF WIND STRESSES UPON THE 
CHORDS AND END POSTS. 

1435. The Upper Chord.—The first condition of item 

(7) of Art. 1399 may be more clearly stated as follows: 

Let W be the computed wind stress in any chord member 

or end post, Z the live load stress, and ) the dead load stress 

inthe same. Also let 4 be the sectional area of the mem- 


ber, computed to provide for dead and live load stresses 
oulyy hen; 
(a) If Ws smaller than ae no change need be made 


an the sectional area A. 





D+L ; 
(6) If Ws greater than - , the sectional area of the 


member should be recalculated by the following formula: 


4,=8A(1+577), (141.) 


wn which A, ts the new sectional area required to provide for 
wind stress. 

It is very seldom necessary, if indeed it 1s ever necessary, 
to increase the sectional area of the upper chord of a through 
bridge, in order to provide for the wind stress in compliance 
with this requirement of the specifications. Inthe structure 
under consideration, the amount of wind stress upon the 
upper chord (omitted from the stress sheet) is 2,560 1b. This 
amount of stress may exist throughout the entire chord as 
compressive stress, or as tensile stress in the center panel. As 
this is much less than one-fourth of the combined live and dead 
48, 600 + 20,800 

4 
provision need be made for the wind stress in the upper 
chord. 


1436. The End Posts.—The first condition of item 
(7) applies also to the end posts. The amount of wind stress 
in the end post is equal to the reaction in the direction of 
the length of this member caused by the wind pressure 
against the portal; that is, the so-called vertical reaction at 


load stresses in the same = = o0071 Domine 


PROPORTIONING THE MATERIAL. 851 


the foot of either end post. This reaction reduces the com- 
pression in the windward end post and increases the com- 
pression in the leeward end post. By reference to Fig. 278, 
itis found that in the structure under consideration this re- 
action, and, therefore, the wind stress in each end post, are 
7,390 lb. As this is less than one-fourth the combined live 
45,800 +19,600 _ 

4 = 
16,350 lb., the wind stress in the same need not be con- 
sidered. 

It is evident that the wind pressure also produces bending 
moment in each end post; this bending moment is greatest 
at the point at which the lower flange of the portal connects. 
In Cooper’s specifications, however, the bending moments 
upon the end posts are provided for in a general way by the 
small unit stresses allowed for those members, and, therefore, 
need not here be further considered. 





and dead load stress in the end post, or 


1437. The Lower Chord.—In considering the effect 
of the wind stresses upon the lower chord, it will be 
well to determine first the amount of stress produced in the 
lower chord by the wind pressure against the upper chord. 
The so-called vertical reaction at the foot of each end post is 
really a reaction exerted 72x the direction of the end post—that 
is, it is a force whose line of action ts represented by the center 
line of the end post, and which resists the force produced in 
the end post, or along the same line of action, by the wind 
pressure against the portal. If the end post is inclined, this 
force has a horizontal component as well as a vertical compo- 
nent. The vertical component simply increases or dimin- 
ishes the vertical pressure upon the support, and is resisted 
by the vertical reaction of the support, but the horizontal 
component must be resisted by stress in the lower chord. 
As the amount of stress in the lower chord is in direct ratio 
to the amount of stressin the end post, it is evident that the 
wind pressure against the portal will diminish not only the 
compression in the windward end post, but also the tension 
in the windward lower chord, while the same wind pressure 


852 PROPORTIONING THE MATERIAL. 


willincrease both the compression in the leeward end post 
and the tension in the leeward lower chord. In other words, 
the horizontal component of the wind stresses in the end 
posts tends to produce compression in the windward lower 
chord and tension in the leeward lower chord. The amount 
FT of the stress developed in each lower chord by the wind 
pressure against the portal is given by the formula 


japeagetics (142.) 


~ b+te’ 

in which P,, is the fota/ lateral wind pressure against the 
portal, f is the panel length, 4 isthe clear width of roadway, 
and c is the width of one chord; i. e., 6-+c is the width cen- 
ter to center of chords. The stress // is constant through- 
out the entire length of each lower chord; it increases the 
tension in the leeward chord and tends to cause compression, 
i. e., diminishes the tension in the windward chord. When 
the compression /7 in the windward lower chord is combined 
with the compressive stresses produced in the same by the 
wind pressure against the lower chord (i. e., as the wind- 
ward chord of the lower lateral system), a reversal of stress 
sometimes occurs and compression is actually produced in 
the end panels of the windward chord. In the present case, 
P.,, the total lateral wind pressure against the portal, is equal 
to 4,050-+ 1,350 = 5,400 lb, (See Fig. 278.) Hence, by 
5,400 X 18 __ 

1i8+1 
5,100 lb. This stress is tension in the leeward chord and 
compression in the windward chord. 





formulas La2s ithe “amount Omest ress re 


1438. fanelab.—By combining this wind stress H/, as 
obtained above, with the wind stresses in the lower chords, 
as found for the lower lateral system and shown on the stress 
sheet, the various stresses that may come upon the end 
panel a 6 of the lower chord are found to be as follows: 


Live load  — 82,400 lb. 
Dead load — 13,900 Ib. 
Wind load eo ect: 


(£40,200 Sal 00 => SOO Ib: 


PROPORTIONING THE MATERIAL. 853 


Of these stresses it will be noticed that the dead load stress 
is always present in the chord; the other stresses are occa- 
sionally present or may be wholly absent. 

The compressive stress upon this panel of the chord pro- 
duced by the wind is equal to 15,300 pounds, and as this is 
greater than the dead load stress upon the same (13,900 
pounds), compression will actually obtain, and, according to 
the second condition of item (/), (Art. 1399), this stress 
must be considered. A portion of this compressive stress 
equal to the dead load tensile stress, simply neutralizes the 
effect of the latter stress, so that the resultant, or net com- 
pressive stress, upon this panel of the chord is + 15,300 — 
13,900 =+ 1,400 lb. By item (s), of Art. 1412, the mem- 
ber must be proportioned to resist each kind of stress, but 
each stress must be considered to be increased by eight- 
tenths of thesmallerstress. Inthiscase, 8, x 1,400 = 1,100 
lb. which added to + 1,400 and — 5,100 gives + 2,500, and — 
6,200, respectively, for the wind compressive and tensile 
stress. As 6,200 is less than oe vont aes the sectional 
area of the member need not be increased. The section 
will be made up of four 3” x 24” angles riveted in the form 
shown at Z, Fig. 303. 


1439. By reference to the details of the connections 
shown in Mechanical Drawing Plate, Title: Highway Bridge: 
Details III, Fig. 1, it will be found that the section cut out 
by two rivet holes must be deducted from the section given 
by each angle. It will be noticed that the lines of rivets in 
the two legs of each angle are staggered; that is, the rivet 
spacing is so arranged that two rivets do not come opposite 
each other in the same angle. When this is done it is not 
uncommon to deduct but one rivet hole from each angle or 
piece, assuming that as the section of the same is reduced by 
but one rivet hole at any normal cross-section its strength is 
reduced only by the sameamount. But, unless the rivet spa- 
cing is exceedingly liberal, the section will be weakened by 
more than this amount, and it is a much better practice to 


S54 PROPORTIONING THE MATERIAL. 


deduct one rivet hole for each line of rivets through each piece. 
This practice will here be followed, and two rivet holes will 
be deducted from each angle. 


1440. When a portion of the sectional area of a tension 
member is cut away by rivet holes, the remaining portion of 
the uninjured metal in the section, which is available to re- 
sist tensile stress, is called the net area or net section. 
The entire section, with no deduction of area for rivets, is 
called the gross area or gross section. As the rivet 
holes are thoroughly filled in driving the rivets, the gross 
area of a member is counted to resist compression, while the 
net area only is counted for tension. 


1441. According to Table 32, Art. 1418, the mini- 
mum weight per foot of a 3” x 24" angle is 4.4 lb., and the 
thickness of metal for this weight is + inch. Assuming the 
metal in the angles used to be of this thickness, the sec- 
tional area to be deducted for eight rivet holes (two in each 
angle) is 2" «45-8175 /$q. 1n., = (See item (4 )eor rune 
1399.) This area must be added to the area required by 
the stresses to give the gross area required for the section. 
Therefore, 3.94 1.5 =5.44 sq. in. is the gross sectional 
area required, making the weight per foot of each angle 
a x ae 4.5 lb. This weight is very little in-excess*of 
minimum weight of 3” x 24” angles (4.4 pounds), and, hence, 
the thickness of metal for this weight of 3” x 24” angle is so 
very slightly more than } inch that the area deducted for 
the rivet holes will be considered correct. If the weights 
per foot obtained for the angles were such that the thick- 
ness of metal would be materially more than the thickness 
assumed in deducting the rivet holes, it would be necessary 
to correct the areas deducted to correspond with the greater 
thickness, and this would again somewhat increase the 
weights of the angles. 

The amount of compressive stress to be resisted by the 
section is 1,400 + 1,100 = 2,500 lb. The dimension W of 
the section is 3+4+3= 63 in., and by formula 113, 


PROPORTIONING THE MATERIAL. 855 


SY, 
Art. L408, the least radius of gyration of the section is ~ x 


Qeeenoein, AS? = [Role ehh in, by taking the 
unit stress for the wind load midway between the live 
and dead load unit stresses, it will equal 15,000 — 60 x 
216 
1.56 





= 6,690 ib. The compressive stress upon this member 


2,500 
6,690 


9 


is thus found to require a sectional area of =e 


sq. in.; it is abundantly provided for. 

The specifications give no compression formula for wind 
stresses upon the chords, but in item (0) the compression 
formula for the allowed wind stress upon the posts gives a 
value substantially midway between the value given by the 
formula for the allowed live load stresses and the value given 
by the formula for the allowed dead load stresses. Hence, 
a formula may be used giving a corresponding value for the 
allowed wind stress upon the chord. 


1442. fanel bc.—By combining the stress /7 with the 
wind stresses given by the stress sheet for the panel 0c of 
the lower chord, it is found that the various stresses which 
can come upon this member are as follows : 


Live load — 32,400 Ib. 
Dead load — 13,900 Ib. 
— 10,200 — 5,100 = — 15,300 Ib 
: c ] i ’ b] 1 b . 
Wind load 4 | 15.300 + 5,100 = +! 20,400 Ib. 


The net or resultant compressive wind stress in this panel 
of the chord is + 20,400 — 13,900 = + 6,500 Ib. As this is 
less than the tensile stress, both the tensile and compressive 
stresses must be increased by eight-tenths of this amount, 
or 48, X 6,500 = 5,200 1b. This makes the tensile wind stress 





W = — 15,300 — 5,200 = — 20,5001b. Asthisis numerically 
D+L 3,90 32,49 , 
greater than ee ae as capt 11,575, the sectional 


area must be recalculated by formula 141. The sectional 
area (A) required by the dead and live load stresses was 


856 PROPORTIONING THE MATERIAL. 


found to equal 3.94 sq. in. (Art. 1403.) Therefore, the 
corrected area (formula 141) is | 


20,500 
> 9 © ? Sea 
rar Pr tare (1 Y 73,900 + 32,400 


) = 4.55 sq. in. 
The section will consist of four 34” x 2” angles riveted to- 
gether in the form shown at JZ, Fig. 303, or in the same 
general formas the member ad. As the required section is 
greater, the thickness of the metal will be somewhat 
greater than in the member ad. A thickness of 2” = .37’ 
will be tried. As the rivets are 2” in diameter, the area to 
be deducted for eight rivet holes (see item (/) of Art. 
1399) is ? xX 2 X 8 = 2.25 sq. in., and the total gross area 
required is 4.55 + 2.25=6.8 sq. in. For this amount of 
sectional area made up of angles of this size, the thickness 
of metal is, quite closely, ie Sie 2) 
near enough to the thickness assumed (.37 in.) to consider 
the area deducted for the rivet holes to be correct. The 
weight per foot of each angle necessary to give this amount 
of section is ee x = mar iparevas 

The amount of compression which the section is to be 
proportioned to resist is 6,500 + 5,200 = 11,700 lb. The 
dimension W is equal to 3}4+4+34=7 in., and by for- 
mula 113, Art. 1408, the least radius of gyration of the 





= -_b2 10,, Whichas 


6 


section is = x 7=1.68in. Using the same compressive 


formula as for a0, the allowed unit stress is 15,000 — 60 x 


216 : 
i e = /,290 lb. The sectional area requiredspyetucmcae 





11,700 
>" — 1.6 sq. in. 
F290 1.6 sq. in., which 


is less than the area given by the section. 


pressive wind stress is, therefore 





1443. Center Panel c c'.—By combining the wind stress 
HT with the wind stresses given on the stress sheet for the 


PROPORTIONING THE MATERIAL. 857 


center panel of the lower chord, the various stresses for that 
panel are found to be as follows: 


Live load — 48,600 Ib. 
Dead load — 20,800 lb. 

_ é — = — 20,400 : 
Meri fe ade y, 100 0,400 Ib 


( +. 15,300 + 5,100 = + 20,400 Ib. 


The compressive wind stress is less than the dead load 
tensile stress. Hence, it can not neutralize the latter or 
produce a resultant compressive stress, and, according to the 
second condition of item (7), it need not be considered. 

But the tensile wind stress (W = 20,400, disregarding the 
sign) is greater than one-quarter of the combined live and 
| Dae .F20,8004-48;600 ae 

4 = 4 —_=] 1,350), 
and, according to Art. 1435, the section must be recalcu- 
lated by formula 141. In Art. 1404, the sectional area 
A was found to equal 5.9 sq. in. Hence, the corrected 

ce iad ) ae th Si. 10; 
20,800 + 48,600 








dead load tensile stress ( 





Atos, St 5.9 (1+ 


1444. As this member is not required to resist com- 
pressive stress, its section could be made up simply by two 
44” x 11” bars, giving a sectional area of 6.19 square inches. 
But it is desired to illustrate another expedient often em- 
ployed when a tension member is required to resist a small 
amount of compressive stress also, namely, that of staying 
or latticing the chord bars together by bent lattice bars. 
The chord bars as thus latticed are shown in Mechanical 
Drawing Plate, Title: Highway Bridge: Details III, Fig. 
3, from which the manner of latticing the bars will be 
readily understood. In order to avoid cutting out too much 
of the section of the chord bar, small size rivets are gener- 
ally used to rivet the lattice bars. In order to avoid injury 
to the metal in the chord bars, the rivet holes are drilled in 
them. When the rivet holes are drilled, it is necessary to 
deduct only the actual size of the rivet hole, which is drilled 
one-sixteenth of an inch larger in diameter than the undriven 


rivet. Inthe present case the rivets will be i in diameter, 


858 PROPORTIONING THE MATERIAL. 


and the rivet hole in the bars will be drilled =,” in diameter. 
The thickness ¢ of the bars may be found by applying the 
following formula: 


Ss 


n(w— day’ Cizisse 


Be ray Dee fe 

nH 
in which S is the sectional area, z is the number of bars 
used, z is the width of one bar, and @ is the diameter of the 
rivet hole, or the sum of the diameters, if more than one 
rivet hole is to be deducted. If the value of ¢ is known, and 
the value of any other one quantity is unknown, that value 
may be readily found by substituting the known values in 
the equation. In the present case, if two bars 44” in width 
are used, by formula 143, the thickness required for each 
bar will be ¢ = ——_>—__ em —=:/8 In. *) The thickness 

2 xX (4.5 — .56) 

used will be the nearest even sixteenth of an inch greater 
than this amount, or 43 of an inch; two bars 44” x 13" will 
be used. By substituting these dimensions in the first form 
given for formula 143, we have 2 = 
solving this equation it is found that the actual net sectional 
area S given by two bars of these dimensions is 6.4 sq. in. 


(4.5 —.56). By 


1445. If a member of this form is required to resist 
compression also, the radius of gyration is found by formula 
140, Art. 1433, d being always the width of one bar. 
This value will always be the /eas¢ radius of gyration of the 
section when y, the perpendiculars between the centers of 
the two bars, is greater than .4 d. 

The value of y is usually so much greater than .4 ad, how- 
ever, that it isseldom necessary to apply the preceding rule. 
As stated above, this member is not required to resist com- 
pression, and could as well be composed of two ordinary 
chord bars of such size as would give the required section, 
without being latticed; they are proportioned with lattice 
bars simply as an illustration. Lower chord members de- 
signed to resist compression as well as tension are often 
called stiffened lower chords. 


PROPORTIONING THE MATERIAL. 859 


EXAMPLES FOR PRACTICE. 


1. What is the least radius of gyration of the lower chord member 
cer Ans. 1.3 in. 


2. What would be (a) the live load unit stress, and (4) the dead 
load unit stress allowed upon this member in compression ? 


(a) 3,350 Ib. 
Ans. } (2) 6,700 Ib. 


PROPORTIONING THE MATERIAL FOR FLOOR- 
ae BEAMS. 


1446. The tensile unit stress allowed in proportioning 
the material for the bottom flanges of riveted floor-beams or 
cross girders is given in item (c), of Art. 1399. The bot- 
tom flanges of simple beams are in tension, while in canti- 
lever beams the upper flanges are the tension flanges. 
Item (c) applies to the ¢exszon flange. In almost all beams 
the tension flange is the bottom flange. The tension flange 
of a riveted beam must be proportioned in compliance with 
item (4), Art. 1399. To items (c) and (£), Art. 1399, 
and (wz), Art. 1412, the following must be added; those 
that have reference to plate girders being applicable to 
riveted floor-beams also: 


(w) ‘‘In beams and plate girders the compression flanges 
shall be made of same gvoss section as the tension flanges.”’ 


(x) ‘‘ Plate girders shall be proportioned upon the sup- 
position that the bending or chord strains are resisted 
entirely by the upper and lower flanges, and that the shear- 
ing or web strains are resisted entirely by the web-plate; 
no part of the web-plate shall be estimated as flange area. 

‘‘The distance between centers of gravity of the flange 
areas will be considered as the effective depth of all 
girders.”’ 

(v) ‘‘The iron in the web-plates shall not be subjected 
to a shearing strain greater than 5,000 pounds per square 
inch, but no web-plates shall be less than three-eighths of 
_an inch in thickness.” 

(z) ‘‘ The webs of plate girders must be stiffened at inter- 
vals, about the depth of the girders, wherever the shearing 


T. JI,.—16 


860 PROPOR TIONING "TPHECMAPERTIATL, 


strain per square inch exceeds the strain allowed by the 
following formula: 

15,000 
PR eRE: 
1 3 900 
where // = ratio of depth of web to its thickness.”’ 


Allowed shearing strain = 


(144.) 


1447. By reference to the stress sheet, the maximum 
flange (designated in item (+) as ‘‘ bending or chord strain ”’) 
in the floor-beam of the example is found to be 53,700 Ib., 
requiring a net sectional area, item (c), Art. 1399, of 
53,700 : 
12,000 
angles to be 2 of an inch in thickness, the amount of sec- 
tional area to be deducted from the gross section for two 
rivet holes (one in each angle) is 2x #x* 2=.56 sq. in. 
Therefore, the gross sectional area of the bottom flange 
must be equal to 4.48+ .56 = 5.04 sq. in., making the 





= 4.48 sq. in. Assuming the metal in the flange 


' weight of each angle equal to os Se : = 6.4. 1b. / \iatwe 
4" x 3" angles are used, the thickness of metal will be very 


closely ae ae 

(4+ 3) x 2 
inch (.388) that the sectional area deducted for the rivet 
holes may be considered correct. The bottom or tension 
flange of the floor-beam will consist of two 4” x 3” angles, 
each weighing 8.4 pounds per foot; and in compliance with 
item (w), Art. 1446, the top or compression flange will be 
the same. 


=.36 in., which is so near to 2 of an 


1448. The latter portion of item (7) specifies that no 
web-plate shall be less than three-eighths of an inch in thick- 
ness. If found to fulfil all other requirements, a web-plate 
2 of an inch in thickness will be used. 

According to Art. 1321, the maximum vertical shear in 
each end of the floor-beam = #, = 20,600 pounds. Accord- 
ing to item (7) of Art. 1446, this shear must be resisted 
entirely by the web-plate, while in compliance with item (7) 
the iron in the web-plate must not be-subjected to a shearing 


PROPORTIONING THE MATERIAL. 861 


stress greater than 5,000 pounds per square inch. The 
maximum shearing stress is a vertical stress of 20,600 
pounds, and the sectional area given by a vertical section of 
the web-plate, after deducting the holes for the two lines 
of rivets connecting the flanges, is 22.5 x 2= 8.44 sq. in. 
The maximum shearing stress to which the metal in the 
20,600 
8.44 
is well within the limit of 5,000 pounds per square inch 
fixed by item (v). A web-plate 2 of an inch in thickness 
will, therefore, be amply sufficient to resist the shear. 
According to item (z) the web of the floor-beam must be 
stiffened if the shearing stress per squate inch exceeds the 
stress allowed by formula 144, Art. 1446. In the pres- 
ent case, /7, the ratio of the depth of web to its thickness, 





web-plate is subjected is = 2,440 lb. per sq. in., which 


is equal to a es 64) cand /7* = 64. 644.096... There- 


fore, the allowed shearing stress per square inch is equal to 
15,000 

iba 

3,000 
the web-plate is subjected has been found to be equal to 
2,440 pounds per square inch, which is well within the lhmit 
of 6,340 pounds per square inch fixed by the same formula. 
It is thus found that a web-plate 2 of an inch in thickness 
will fulfil all requirements of the specifications without 
stiffeners being used. But it is desired to illustrate the use 
of stiffeners, and, therefore, though not required on this 
beam, they will be used. <A web-plate for this floor-beam 
4 of an inch thick would probably require stiffeners. This 
thickness is not uncommonly used for web-plates of light 
floor-beams. 


= 6,340 pounds. The shearing stress to which 


THE FLOOR. 


1449. The following items of the specifications have 
reference to the general features of the structure, but 
especially to the floor system: 


(A) ‘‘All parts of the structures shall be of wrought 


862 PROPORTIONING TEM eva ET hoa, 


iron or steel, except the flooring, floor joists, and wheel 
guards, when wooden floors are used. Cast iron or steel 
may be used in the machinery of movable bridges, and, in 
special cases, for bed-plates.” 


(2) ‘‘For all through bridges there shall be a clear 
head-room of 14 feet above the floor.” 


(C) ‘*The floor joists will generally rest upon transverse 
iron floor-beams. They will be spaced not over 2 feet cen- 
ters, and will lap by each other, so as to have full bearings 
on the floor-beams, and will be separated 4 inch for free cir- 
culation of air. Their scantling will vary in accordance 
with the length of panels selected, but shall never be less 
than 3 inches wide.” 


(D) ‘‘The floor plank shall be—inches thick, laid with 
1 inch openings, and spiked to each supporting joist. When 
this is to be covered with an additional wearing floor it must 
be laid diagonally; all plank shall be laid with the heart 
side down.” 


(£) ‘‘For bridges of classes d and Z an additional wear- 
ing floor 14 inches thick of white oak plank shall be placed 
over the above.”’ | 


(f°) ‘*Where a foot-walk is required it will generally be 
placed outside of the trusses, and formed by longitudinal 
wooden joists, supported on wrought-iron overhanging 
brackets. The plank will be 2 inches thick and not over 
6 inches wide, spaced with # inch openings.”’ 


(G) ‘*There will be a wheel-guard, of a scantling not 
less than 4” x 6’, on each side of the roadway to prevent 
the hubs of wheels striking any part of the bridge. The 
roadways will be 12 feet wide for a single track, and multiples 
of 10 feet fora greater number of tracks.”’ 


(/7) ‘‘A substantial railing will be placed at each side 
on all deck bridges. In through bridges the openings in the 
trusses must be closed by an iron railing of a suitable form; 


PROPORTIONING THE MATERIAL. 863 


there must be a substantial hand rail on the outside of the | 
foot-walks.”’ 


(7) ‘*The maximum strain allowed upon the extreme fiber 
of the joist will be 1,200 pounds per square inch on yellow 
pine and white oak, and 1,000 pounds per square inch on 
white pine and spruce.” 


(A) ‘‘ When iron or steel joists are used they must be 
securely fastened to the cross floor-beams. The floor plank 
must have a thickness, 27 zzches, at least equal to the dis- 
tance apart of these joists, zz feet. The floor plank must 
bear firmly upon the iron joist and be securely fastened to 
the same.”’ 


(L) ‘‘In calculating strains, the length of span shall be 
understood to be the distance between centers of end pins 
for trusses, and between centers of bearing plates for all 
beams and girders.” 


It will be noticed that in the design which has been taken 
as an example, item (/) and the latter portions of items 
(G) and (/7) have not been complied with, while items (/’) 
and (A) do not apply to this design. Item (£) is not 
very generally complied with. Many engineers consider 
that the tendency of the two layers of plank to retain 
moisture and thereby hasten decay, is greater than the 
advantage derived from the additional wearing floor. 
Probably the plank floor most commonly used for the 
roadways of bridges consists of a single layer of plank 3 
inches in thickness. This thickness for the roadway floor 
plank has been found to give very satisfactory results in 
ordinary highway bridges, and for such bridges has been 
very extensively used. The roadway floor plank, if of a 
single layer, should not usually be less than 3 inches in 
thickness, and should not under any circumstances be 
less than 24 inches thick. When of the latter thickness, 
hard lumber should always be used. In the example, 
the floor plank is 3 inches thick and the wearing floor is 
omitted. 


864 PROPORTIONING THE MATERIAL. 


1450. The dimensions of the joists vary with their 
span; that is, with the length of the panels. The most 
common varieties of timber used for joists are long leaf 
yellow pine (known also as southern pine and hard pine), 
white oak, white pine, and spruce. A very excellent timber 
known as Oregon fir is also being extensively used in the 
West. This timber may be considered as equivalent to long 
leaf yellow pine. It is generally accepted as good engineer- 
ing practice to allow for timber in flexure a modulus, or 
assumed stress in the extreme fiber, of 750 pounds for white 
pine or spruce, 1,000 pounds for white oak, and 1,200 pounds 
for long leaf yellow pine. 

Timber joists are usually spaced 2 feet apart from center 
to center. ‘This is the common practice, and it is also in 
accordance with item (C). Table 33 gives the dimensions 
for joists, spaced 2 feet apart, center to center, required to 
sustain a total uniform load of 100 pounds per square foot, 
assuming the extreme fiber stresses to be 1,200 pounds, 
1,000 pounds, and 750 pounds for long leaf yellow pine, 
white oak, and white pine, respectively. It will be noticed 
that in this table two widths are given in each case. The 
upper dimension is the calculated width, while the lower is 
the practical width to be used. For loads greater or less 
than 100 pounds per square foot, or for spacing greater or 
less than 2 feet, center to center, use widths proportionally 
greater or less than the computed (upper) width in each 
case given. | 

Item (C) of Art. 1449 requires that joists shall never 
be less than three inches wide. It is also not considered to 
be good engineering practice to use joists having widths 
less than one-quarter of their depths. It will be noticed 
that in a few cases both these conditions are violated in 
Table 33. When joists having depths greater than four 
times their widths are used, it is customary to brace them 
laterally by means of small pieces connecting the bottom of 
each joist with the top of each adjacent joist. Such 
bracing is called bridging; it is placed at the centers of 
the joists and at intervals of a few feet along their length. 


PROPORTIONING THE MATERIAL. 


TABLE 33. 


Dimensions of Timber Joists or Stringers, spaced 2' 0" 
apart, center to center, required to support a untformly dis- 
tributed load of 100 lb. per square foot. 








Panel 





865 
































Length. Yellow Pine. White Oak. White Pine. 
Feet. Inches. Inches. Inches. 
po ve Th RSL) A 12 SR ely) eke Se 
Width. Depth. Width. Depth. | Width. Depth. 
9 | 228P x10 | 288) sexo | MO} 
13 | a505 X1 | sof x 1° | sof x2 
14 | Soot % 19 | so0f X® | asof X22 
[ASE as [BEE x | BBE xu 
16 | so0f X12 | sof X12 | s50f x ¥ 
1 | oof X22 | xoof X14 | ago X14 
| BE ae | B88 a | BE cu 
BOE Nps Went Petey OC Ue) Hota) oe de. . 
Sh ele og hee naa. s ts 
Pe Messi fe iid) sek cesktb. 02604 a 
1451. The number of lines of timber joists spaced 


2 feet apart, center to center, required to support a road- 
way floor of any width is given by the formula 


b 
Sage i te 


(145.) 


in which wz is the number of lines of joists, and 6 is the 
clear width of roadway in feet. 
In the example the floor is assumed to be of yellow pine 


866 PROPORTIONING THE MATERIAL. 


timber. From Table 33 it is found that, with panel lengths 
of 18 ft., 34” x 12” are the dimensions required for joists of 
this material. 

For a clear width of roadway of 18 feet, according to 


formula 145, there will be = +1=10 lines of joists, as 


shown in Mechanical Drawing Plate, Title: Highway Bridge: 
General Drawing. These joists are spaced nominally 2 feet 
apart between centers, but really somewhat less than this. 


EXAMPLE.—For a width of roadway of 16 feet and a panel length of 
14 feet, what are (a) the number of lines, and (4) the dimensions required 
for white oak joists spaced 2'0" apart, center to center, to support a 
uniformly distributed load of 120 pounds per square foot ? 

SoLuTION.—(a) According to formula 145, there will be a) +1= 


9 lines of joists. Ans. 


(6) From Table 33, the computed dimensions of white oak joists to 
sustain a uniform load of 100 pounds per square foot upon a panel 
length of 14 feet are 2.46" « 12”. For a uniform load of 120 pounds per 
square foot the required width of the joists will be 2.46 x 1.20 = 2.95 
in. ‘The dimensions required for the joists will be 3" x 12”. Ans. 


EXAMPLES FOR PRACTICE. 
1. Fora width of roadway of 14 feet, how many lines of joists will 
be required, if spaced 2’ 0", center to center ? Ans. 8 lines. 


2 If the panel length is 18 feet, and long leaf yellow pine is used, 
what will be the dimensions of the joists required to support a uniform 
load of 90 pounds per square foot ? AnS.. So4elee 


3. The width of roadway in a bridge is 16 feet, and the panel 
length is 15 feet. (a) How many lines and (4) what dimensions of yel- 
low pine joists spaced 2’ 0", center to center, will be required to support 
a uniform load of 125 pounds per square foot? nN BS 9 lines. 

Me Ope ePL, 


COMPLETING THE STRESS SHEET. 


1452. The formand size of the material have now been 
determined for each member of the bridge, taken as an ex- 
ample to illustrate the general method of proportioning the 
material. In Fig. 306 is shown a complete stress sheet for 
the bridge... It is similar to Figs 283, Artest Secenumt 
gives in addition the sections and general dimensions of the 


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ee SHIPPING BILL. 
eee a cia ea) Sc rere gh ene ME een ae COMETACESING oe aoe $ 
oe Siete eet, OC. toc, St DeO Wee gee tga eae eee ae 
sonzeccnanoenam Roadway............ feet, clear width. PE ie Oe. S70 RM Oe ac im ME EL eel os ane eS 
tnvenneseneeence Sidewalks... feet, clear width. ‘VEL ERR» P08 2. SED nrne eee aarene ace nr o P ne Wes = 
| No. and Shippin 
No. Re- N f aoe pping 
Mark. Oe nee ees Material in Member. ae Length. Weight. 
) : { 2-R| ( 1-Plate 12” « 34" | 2-228 O5.- 6,565. Canter Ge 
fae fo Ane Boats 1 2-L | ( 2-8” Chans. @ 16 lb. : 
. § 2-R| ( 1-Plate 12" x Y" 1-225" | 17° 8%" C. tok. 
eG 4 |Top Chords 1 2-L | ] 2-8” Chans. @ 11 |b. me | ( 18’ 03" C, oe 
s z \7-Plate 12" x 2 eee) | 18-896 Beto 
se Bey nerds ) 2-8” Chans. @ 11 Ib. | : 
: Aerts Posts 4-31%4" X 2" L’s @ 4.4 lb. Latticed 1-225" Py lg Ce to de, 
BB, 2 cer ad eae 4-314" KX 2%" L’s @ 4.8 lb. Latticed 20) SO ag Eee 
a 2 |Lateral Struts 2-5" x 4” L’s @ 10.8 lb. 20! Qe ¥ E. to’ E. 
eB 4 |Knee Braces 2-3' X 24%" L’s @ 4.4 lb. Aaa. beto DB: 
aa {1-Piate-G So ye 1D 104621; to-k. 
aay t |Shoe Strut (23/4 een Me io | oe ae 
aaa) > = 1-Plate 24" X 36" me a2 : 
FB 4 |Floor-Beams 4-4" X 3" L’s @ 8.4 lb. | = Sas - 
vine ae 8 |Beam Hangers 14%" X1\%", 1%" S. Ends with Check Nuts T-255 2 eee B. to E. 
iT f 8 |Hanger Pls. 6exX 3" 2-2" o 434° ©. to C. 
Ro) 4 |Separators Bt ee 2-2". |. @ 4%" C. to C. 
ab 4 |Lower Chords 4-3" x 214" L's @ 4.6 Ib. Latticed 2-255" 17 1133" C. to C. 
Be Fs 4  |Lower Chords 4-3%" x 2" L’s @ 5.8 lb. Latticed 2-255" 17 1133" C. to C. 
Roe 2 |Lower Chd. Bars 2 Bars 4%" X 18" Latticed 2-255 17 1133 C. to C. 
Pe 8 /Tie Bars 2 ae | 2-253. 25' Sie. Cato 
B=o 8 |Hip Vert. Rods Teer” 2-253" 18 253" B. to B. 
ee 8 |Counters hh" xX 7", 13%" S. Ends 1-128 20! 3'5 Batock:. 
eg 8 |Counters Va are re Ends, 934" Turnbuckle 1-233" Ea B. to E. 
a b, 4 !Lateral Rods (ee Cas Oe faa Yar ain ota | 1-158" 19 84" B. to E, 
ab, 4 |Lateral Rods 1%" QO, 1%’ S..Ends, ro’ Turnbuckle | 1-133 5.0 S Bint is 
OEE 6 |Lateral Rods On 2134" 8. Ends T-153" 19° 7%" B. to E. 
tee 6 |Lateral Rods rt "O, 1%'S. Ends, 93" Turnbuckle _I-1 33 5 0 - B.to E. 
BC, | 4 |Lateral Rods tO; Stee ends St. Nuts] 25’ 105" E. to E. 
Cs 2 |Lateral Rods Im, 13% 5. nde Si Nuts 26° 214" E. to E. 
a 4 |Chord Pins 234" 0, 115%" Grip R. Nuts | 1 238" E, to E. 
B, b, ¢ 12 Chord Pins 237° ©9037" Grip R. Nuts Pe be Om” E. to E. 
C 4 (Chord Pins 1X" Ox 9% Grip R. Nuts o 11%" E to E. 
Li 20 |Lateral Pins 134.4), 294 - Grip, OCdtters Os» Eto E. 
& 4 |Pin Washers For 1 oe Pin o 64" E. to E. 
LB 4 |Pin Washers For 23/" Pin o 2" E. to E. 
b 8 |Pin Washers For 234" Pin Crete: E. to E. 
b 8 |Pin Washers For 23/". Pin | ie ee K.. t07R:, 
Ginae femiang 7% 3 1A” ee ee L's /§ 2-253" | 
gae\ ne hOrualoes Drie “17%34' <. BB" * 13 swith Latecon, jo T-1t3" | 
wie Stand, 7°. x. 972 2 se L's | § 2-253" | 
ae {Roller Shoes UPL. 22714 See eeaohoe St. & Lat: con. |] 1-142 
2 /|Nests Rollers Di, 174 x 14" | 
2 |Bed-Plates Si wees ae TA ; | 
2-— 1 bent Aen, Pis. er ee ae x 33% 1-176" | 
12 |Anchor Bolts Ee O X to’ with Wedges 
20 |Field Kivets 78" Cy 234" Wika oF | 
20 |Field Rivets ree OF See U: a | 
Peso. [Field Rivets %" OX 2%’ U..4B3 
50 |Field Rivets 5" Cox 176! U3 
150 |Field Rivets 8" OX 1% Lear: : 
32. »\Bolts 4% O X_I0 Te & 270 
Spikes 6" Steel Wire 7 
Nails 4%" Steel Wire 
Paint : F 
160 |Erection Bolts %” O X2 & LE 
40 |Erection Bolts 4%" O X1%" U. H. 
Pilot Nuts For 23¢" Pin 
Pilot Nuts For 134" Pin 

































































PROPORTIONING THE MATERIAL. 867 


material. The material for each respective member is shown 
written along the member in the vzg/¢ half of the diagram 
of the truss and along each web member in the diagram of 
the lateral systems. 

It will be noticed that in this stress sheet the stresses are 
omitted from all members of the lateral systems except the 
diagonal members. ‘The effects of the lateral wind stresses 
upon the chords of the lateral systems are considered in 
connection with the live and dead load stresses in the chords 
of the truss; they are, therefore, sometimes written with the 
live and dead load stresses, but are much more commonly 
omitted. As the lateral struts are proportioned by the 
resultant of the initial stresses assumed upon the attaching 
rods, the wind stresses in those members need not be con- 
sidered, and are usually omitted from the stress sheet. 

The complete data for the bridge are written below the 
diagrams, asin the former stress sheet, with additional in- 
formation designating the kind of material used and the 
specifications by which the material is proportioned; also, 
the kind and dimensions of the material for the floor. Some- 
times, also, the location of the bridge and the name of the 
designer or builder are placed in the lower right-hand corner 
of the sheet. 

The stress sheet as thus completed is intended to convey 
all necessary information with reference to the general 
design of the superstructure of the bridge ; it may be taken 
as a basis for receiving or submitting proposals or making 
the contract for the construction of the same. Toa bridge 
engineer it gives nearly all the information relating to the 
superstructure that is necessary for making an estimate of 
the cost. It does not, however, give any information in 
regard to the details and connections, other than to desig- 
nate the specifications by which they are to be proportioned, 
which is sufficient for the purposes of an estimate. Some- 
times the stress sheet does not designate any general speci- 
fications, but is attached to, or accompanied by, a set of 
specifications drawn especially to suit the requirements of 
the structure for which the design is made. 


868 PROPORTIONING THE MATERIAL. 


1453. In making the complete stress sheet the student 
should follow the general arrangement shown in Fig. 306. 
The stress sheet should always show a side elevation of the 
truss anda half plan of each lateralsystem. Sometimes, for 
important structures, larger, stress sheets are made, upon 
which are also drawn end views, showing the portal bracing, 
and intermediate lateral sections, showing the intermediate 
sway bracing, floor-beams, and connections. 

In completing this stress sheet, write correctly, to one 
decimal place, the weight per foot of each rolled shape 
used, and write the sectional area of each entire section, 
using two decimal places, except in case of riveted tension 
members, for which write the zet sectional area, following 
it by thewet terse: so: 

The weights per foot of plates and of round, square, or 

flat rectangular bars are not usually written. When the 
different portions of a built member are connected by means 
of lattice bars, the word ‘‘latticed”’ should be written 
beneath the member. 
_ The thickness of the floor plank, the material of which it 
is composed, the number of lines, dimensions, and material 
of the joists, and the material and dimenSions of the wheel 
guard should be given on the stress sheet, and also all 
other important conditions or lata relating to the design. 


THE USE OF STEEL. 


1454. The members of a bridge are proportioned in 
steel in the same general manner as when proportioned 
in wrought iron. The unit stresses and compression formu- 
las are somewhat different, but, otherwise, the process is. 
substantially the.same. The observations concerning the 
forms of tension members (Arts. 1399 to 1401), and 
the formulas for the relative dimensions of compression 
members and for the radii of eyration ofthe *direroat 
forms of sections (Arts. 1407, 1408, 1413, 1414, 
1419, and following) apply to steel as well as to iron. 

Soft steel (Art. 1388) is probably the best and most | 


PROPORTIONING THE MATERIAL. 869 


thoroughly reliable material for bridges. But medium 
steel is somewhat stronger than soft steel, and, being 
allowed higher unit stresses, is, therefore, more economi- 
cal. As medium steel is also quite reliable, it is the material 
commonly used for bridges at the present time. 

Specifications for the use of soft steel and medium steel 
“vary even more than those for iron. The use of high steel 
in bridges is not usually either specified or allowed. A few 
of the common and prominent features of the specifications 
for the use of structural steel will now be noticed. 


COOPER’S SPECIFICATIONS. 


1455. In Cooper’s General Specifications for Highway 
Bridges, the use of soft steel and medium steel is based 
upon the practice specified for wrought iron. The speci- 
fications referring to the use of steel are brief, and are 
here quoted in full. They are as follows: 

‘“Medium steel may be used for tension members, plate 
- girders, rolled beams, and top chord sections with an allow- 
ance of 20 per cent. increase above allowed working strains 
on wrought iron; and for all posts by use of the following 
formulas, in place of those given for wrought iron: 


P= 10,000 — 70 for live load strains. (146.) 
P= 20,000 — 140 4 for dead load strains. (147.) 
P= 16,000 — 103 for wind load strains. (148.) 


‘*Provided, that, in addition to the previous details of 
construction (1. e., those given for wrought iron), all sheared 
edges of plates and angles be planed off to a depth of one- 
quarter of an inch. All punched holes be reamed to a 
diameter of inch larger, so as to remove all the sheared 
surface of the metal.”’ 


870 PROPORTIONING THE MATERIAL. 


1456. ‘‘No sharp or unfilleted re-entrant corners to be 
allowed.”’ 


1457. ‘‘All rivets to be of steel.” 


1458. ‘‘Any piece which has been partially heated or 
bent cold be afterwards fully annealed.” 


1459. ‘‘Soft steel may be used under the same con- 
ditions as wrought iron for all rzveted work. 

‘¢Provided, that any rivet hole punched, as in ordinary 
practice, will stand drifting to a diameter 25 per cent. 
greater than the original hole without cracking, either in 
the periphery of the hole or on the external edges of the 
piece, whether they be sheared or rolled.” 


1460. It will be noticed that while by the above speci- 
fications. medium steel in tension members and in com- 
pression chord members is allowed unit stresses 20 per 
cent. greater than those allowed wrought iron, in posts it is 
quite otherwise. For short struts the unit stresses allowed 
- by the compression formulas for steel posts are greater 
than those allowed by the compression formulas for iron 
posts, while for long struts the formulas give less unit 
stresses for steel than for iron. The live and dead load 
unit stresses allowed by the post formulas for steel are 
greater than those allowed for iron when the strut length 
is less than 624 times its radius of gyration, but they are 
less than those allowed for iron when the strut length 
exceeds 624 radii. 


For the value given by the iron formula 8,750 — 04 
becomes equal to the value given by the steel formula 


10,000 — 0-4, when the quotient equals 62.5; and the 


V4 
former value exceeds the latter when exceeds this amount. 


Many engineers consider this specification for medium steel 
to be unnecessarily severe. Most specifications allow greater 
unit stresses for soft steel than for wrought iron. 


PROPORTIONING THE MATERIAL. 871 


EXAMPLES FOR PRACTICE. 


See stress sheet, Fig. 306. 

1. If medium steel is used, what is the sectional area required fo1 
the main tie bar Bc? Ans. 2.7 sq. in. 

2. What size of bars will give the required area for this member ? 

3. What is the sectional area required for the counter Cc’, if com- 
posed of medium steel ? Ans. 1.15 sq. in. 

4. Of what should this member consist in order to have the 
required area ?_ 


5. Using 8-inch channels of medium steel, what is (a) the live load 
unit stress and (4) the dead load unit stress allowed for the upper 
chord ? Ans. } (a) 8,760 lb. 

(6) 17,520 1b. 

6. What is the sectional area required for the upper chord ? 

Ans. 6.74 sq. in. 

7. What is (a) the live load unit stress and (4) the dead load unit 
stress allowed for the end post, using the same size of steel channels ? 

Ans, § (@) 8,815 Ib. 
( (4) 6,630 Ib. 

8. What is the sectional area required for the end post ? 

Ans. 16.78 sq. in. 

9. What is (a) the live load unit stress and (4) the dead load unit 
stress allowed for the intermediate post, using 34" « 2" angles of 
medium steel ? rer § (a) 1,600 Ib. 

l (4) 8,200 Ib. 

10. What sectional area is required for the intermediate post ? 

Ans. 6.78 sq. in. 


REMARKS. 


1461. A comparison of the preceding results with the 
corresponding results as previously obtained for iron sec- 
tions will be found instructive. It will be noticed that the 
sectional areas obtained above for the tension member and 
for the upper chord are less than obtained for the corre- 
sponding members when proportioned in iron, while those 
obtained for the posts are greater than for the iron posts. 
This feature of these specifications is by many engineers 
considered to be inconsistent and objectionable. 


1462. In designing bridges, according to Cooper’s 
specifications for medium steel, it is always advantageous 
to make the heights of truss somewhat lower than would 


872 PROPORTIONING TAT Nira aa, 


ordinarily be used in designing by most other specifications. 
This statement applies to iron as well as to steel, though in 
a less degree. When designing a bridge having parallel 
chords, according to Cooper’s specifications for medium 
steel, a height of truss equal to about one-seventh the span 
will usually afford good economy. 

In the example for which the material has been propor- 
tioned in iron, if the height of truss had been taken as low 
as the required head-room would permit, say 15 ft., the 
sections of the top chord and end post would have been 
more nearly uniform. The sections required for the chords 
would be increased by reason of the increased chord stresses, 
while the sections of the posts would be diminished by reason 
of the diminished strut length. The dead load stresses in 
the lower chord would be increased, while the wind stresses 
would be somewhat diminished. 


THE FATIGUE OF METALS. 


1463. What is ordinarily called the w/tzmate strength of 
a material is the greatest stress to which it can be subjected by 
a force applied gradually and for a moderate length of time ; 
it occurs at or just before rupture. Experiments, however, 
have shown that when forces below the ultimate strength 
are constantly or repeatedly apphed, they may finally pro- 
duce rupture; their effect) seems) to be to exhaust: the 
material, or to ¢zre zt out, so to speak; whence the name 
fatigue of metals is applied to this phenomenon. Later 
experiments have shown that the true cause of the phenom- 
enon lies in the imperfections and lack of homogeneity of 
the material. 


1464. The following law was discovered by A. Woehler, 
after a series of experiments, and is known as Woehler’s 
law: 


Rupture may be caused not only by a force exceeding the 
ultimate strength, but by the repeated or prolonged action of 
forces below the ultimate strength. When these forces are 
alternately applied, the unit stress that finally causes rupture 


PROPORTIONING THE MATERIAL. 873 


depends upon the range of stress, that ts, upon the difference 
between the alternately applied forces. As this difference tn- 
creases, thenumber of applications necessary to produce rupture 
becomes Less. 


Thus, wrought iron was found to fail after 800 applications 
of a tensile force of 52,000 pounds per square inch; also, after 
409,000 applications of a tensile force of 39,600 pounds per 
square inch. With forces alternating between 22,000 and 
48,400 pounds per square inch, the number of applications 
required for rupture was nearly 2,400,000; whereas, with a 
range between 26,400 and 48,400 pounds per square inch, 
4,000,000 applications were made wrethout producing rupture. 
In the two cases last mentioned, although the higher limit 
of stress was the same (48,400), the effects were different, 
owing to the difference in the range, 48,400 — 26,400 being 
less than 48,400 — 22,000. In some cases rupture (by bend- 
ing) has been produced by the repeated application of a load 
of only two-fifths the breaking load calculated from the ul- 
timate strength; a bar that could stand a gradually applied 
load of 26,000 pounds broke under a load of 10,480 pounds 
after 5,200 applications. 

1465. The preceding facts are of great importance in 
the design of such structures as bridges which are subjected 
to varying stresses, whether of the same or of opposite kinds; 
and it will be readily seen that the resistance of a member 
can not be accurately determined from considerations of 
ultimate strength only, but the phenomenon of fatigue must 
be taken into account. 

When a member is subjected alternately to stresses of the 
same kind (all tension or all compression), the allowed or 
working unit stress ? (pounds per square inch) 1s commonly 
taken as given by the following formula: 


Weal (1 ao 


When the alternating stresses are of different kinds, 


) (150.) 


(149.) 


minimum. Stress 
maximum stress J 


maximum stress of smaller kind 
2X maximum stress of greater kind 





paa(1— 


874 PROPORTIONING PRE SMA eet. 


In both of these formulas @ is a constant depending on the 
material and on the kind of stress. The value of ais not 
necessarily the same for the two cases considered. 

Other and more accurate formulas have been constructed, 
but those here given are the ones required by some of the 
most modern specifications. 


1466. Of specifications founded on the theory of the 
fatigue of metals, those of Mr. Edwin Thacher for highway 
bridges may be mentioned. In them formula 149 is used 
for tension members, with the following values for a: 














Values of a. 





Member. Wrought Soft Medium 
Iron. Steel. Steel. 








Chords, ties, counters, long sus- 
PENCers 5 iid ena: aed eee 9,400 10,800 | 11,700 
Platéssandshapese. a eee 8,500 9,700 | 10,500 

















For members in which tension and compression alternate, 
formula 150 is used, with 


9,400 for wrought iron, 
a 2 91 0 ROUstorisoltetvedh, 
11,700 for medium steel. 


Other members are proportioned by ordinary formulas, 
which, although giving somewhat different values from those 
we have used, involve no new principles. 


EXAMPLE.—What are, according to Thacher’s specifications, the 
unit stress allowed for hip vertical # d (Fig. 306), and the required 
area (a) when the member is to be of wrought iron, and (4) when the 
member is to be of medium steel ? 


SOLUTION.—Since the hip vertical is a long suspender, formula 149 
must be used, with the values of @ given above for tension members. 
By reference to Fig. 306, it is found that the minimum stress to which 
the member is subjected is 4,600 pounds (when the truss is unloaded), 
while the maximum stress = 16,200 + 4,600 = 20,800 Ib. (when the truss 
is loaded). These values in formula 149 give, calling the required 


PROPORTIONING THE MATERIAL. 875 


area A, and remembering that required area = total stress + allowed 
unit stress : 








(a) P= 9,400(1 + eae = 11,480 Ib. 
= ae = 1.81) s8q.)in. 

(3) P =11,700 (1 + a a00) = 14,290 Ib. 
= we = 1.46 sq. in. 


SOME ITEMS FROM THACHER’S AND LEWIS’S 
SPECIFICATIONS. 

1467. The requirements of the many specifications in 
existence are very different; but, if the student has mas- 
tered the general principles on which they are founded, and 
the general methods by which they are applied, he will ex- 
perience no difficulty in adapting his knowledge to the 
different requirements; the question is simply one of 
substituting different values for the constant quantities 
contained in a few general formulas. 

Some items not before mentioned are of importance, and 
they are here quoted from the specifications of E. Thacher, 
and those of F. H. Lewis. 


1468. From Thacher’s Specifications for High- 
way Bridgés.—‘‘ Clearance. All through bridges shall 
have aclear height of not less than 14 feet.”’ 


1469. ‘‘The width from c toc of trusses shall not be 
less than one-twentieth of the span from ¢ to ¢ of pins.”’ 

NotTe.—c stands for center. 

1470. ‘‘ Flanges.—The compressed flanges (of girders) 


will be stayed transversely when their length is more than 
thirty times their width.” 


1471. ‘‘ Weds.—One-sixth of the web will be considered 
as available area in each flange, except at web splices, where 
the full section will be provided by extending the flange 


ZL. lI,—17 


876 PROPORTIONING THE MATERIAL. 


plates, or by the addition of separate cover plates. All 
joints will be spliced by a plate on each side of web.” 


1472.  ‘‘ Stiffencrs.—All web-plates shall be stiffened 
at the inner edges of end bearing, and at all points of local 
concentrated loadings. Intermediate stiffeners will be used 
if the shearing stress per square inch exceeds 12,000 + 





Le ; 
(1 + 3 aa) in which @=clear distance between flange 


angles or stiffening angles and ¢= thickness of web, both 
i ING ie sna 


1473. Timber.—For beams, allowed fiber stress for 
yellow pine and white oak, 1,200 pounds per square inch; 
for white pine or hemlock, 900 pounds per square inch. 


1474. For timber struts, the allowed unit stress shall 
be determined by the following formulas: 








Yellow Pine. White Pine. 








HSE ON CS. c.f cet er eae ees 1,075 — 112% 675 — Ver 

a a 

dB Nas gs b 

One fatand one pinienc a. 1,075 — 125, O75 — 100 — 
€ (g 

Pin .endsie ss sles oes 1,075 — 138 675 — Oe 














e, \ = leneth ofanembelevayecs 

In which ; ; ; adie 

( a= least dimension of member 7x zuches. 
1475. The following are the allowed unit stresses for 


shearing and bending: 











Yellow Pine. White Pine. 





Shearing—Sliding on grain... 130 100 
Bearing — Direction of grain.. 1,200 900 


Perpendicular to 
AIT ate ogee ee 300 200 





PROPORTIONING THE MATERIAL. 877 


1476. From Lewis’s Specifications for Railroad 
Bridges.—‘“‘ Superstructure.—For spans of 16 feet or less, 
rolled beams will be used, and from 16 to 100 feet, riveted 
plate girders. _ All spans over 100 feet will be pin-connected 
LEUSSES, 


1477. Material Used.—lit is required: 


‘‘1, That all eye-bars and pins shall be of medium steel. 

‘¢2. That all web-plates shall be of steel. 

‘¢3. That loop rods and all other devices which are welded 
shall be of wrought iron. 

‘‘These requirements are common to all bridges, whether 
built of wrought iron, soft steel, or medium steel. The 
other parts of bridges, however, may be built of such grades 
of material as the contractor may elect, provided only that 
each member and each set of members performing similar 
functions must be of the same grade of material throughout.”’ 


1478. ‘Dead Load.—The dead load shall consist of the 
entire structure. The load of the structure when complete 
shall not exceed the dead load used in calculating the stresses.”’ 


1479. ‘In through bridges, two-thirds (%) of the dead 
load shall be assumed as concentrated at the joints of the bot- 
tom chord, and one-third (4) at the joints of the upper chord.” 

1480. ‘‘In deck bridges, two-thirds (%) of the dead load 
shall be assumed as concentrated at the joints of the upper 
chord, and one-third (4) at the joints of the bottom chord.” 

1481. ‘Plate girders shall be proportioned upon the 
supposition that the bending or chord strains are resisted 
entirely by the upper and lower flanges, and that the shear- 
ing or web strains are resisted entirely by the web-plate.”’ 

1482. ‘Stiff suspenders must be able to carry a com- 
pressive strength equal to six-tenths (,°,) the maximum 
tensile stress.” 


1483. ‘‘Stiffened chords will be proportioned to take 


ry. 


compression equal to 60—, in which 7 is the maximum ten- 


Wh b] 
sion in pounds in the chord, and Z is the span in feet.” 


878 PROPORTIONING THE MATERIAL. 


1484. ‘‘Coeffictents of friction will be used as follows ; 


‘“Wrourht ron oresteel Ontitsel ivan. tire 15 
’ Wrought iron-on steel cn castrirony vas. es 20 
‘COMirourht-ironior steel onvmasonry: enter 25 
“Masontyeoneitsell. 7.00. neh oes 200% 


COMPARATIVE WEIGHT AND SPECIFIC GRAV- 
ITY OF WROUGHT IRON AND STEEL. 


1485. The specific gravity, and, therefore, the weight 
of both wrought iron and steel, vary according to the 
purity of the metal, and also according to the density 
imparted to it by the process of rolling. 

As a rule, soft steel possesses somewhat higher specific 
gravity than high steel, while both are denser than iron. 

The following tables give fair average values of the spectfic 
gravity and weight of wrought tron and these two grades 
of steel; 

TABLE 34. 


ORDINARY SMALL ROLLED BARS. 








Weight per Weight per 





























Material. pone Cubic Foot, Cubic Inch, 
lp Pounds. Pounds. 
SOLE soLee lemmas 7.86 |; 490.1 2836 
Poh Steele meee, 7.83 488.2 2825 
Wrougnte lone: scr 7.70 480.1 ie 
TABLE 35. 
LARGE ROLLED SECTIONS. 
: ; Weight per Weight per 
Material. eee Cubic Foot, Cubic: Inch, 
y Pounds. Pounds. 
SO fan leelin hoes er 7.84 489.0 .2830 
Mighes teels yi. 7.80 486.6 .2816 


Wirouchtelron, ea 7.67 478.3 2768 








PROPORTIONING THE MATERIAL. 879 


1486. As statedin Art. 1415, it is customary to esti- 
mate the weight of rolled iron at 480 pounds per cubic -foot, 
which is believed to be practically correct for the average 
material. No allowance is made for the slight decrease in 
the weight of large sections. 

Medium steel, having properties about midway between 
those of soft steel and high steel, will average about 2 per 
cent. heavier than iron. It is customary to estimate all 
grades of structural steel 2 per cent. heavier than iron. 

Upon this basis the following values are obtained for 
steel: 

By adding 2 per cent. to the value of w in formula 132, 
Art. 1415, the following value of JV, the weight per lineal 
foot of a bar of steel, is obtained: 





Wa A %1.02=34A.  (151.) 
Similarly, A= us (L352) 


In both of the above formulas, 4 is the sectional area of 
a steel bar of any shape having a uniform cross-section, 
i. e., the sectional area of any rolled steel bar. 


EXAMPLE.—A bar of steel has a sectional area of .4418 of a square 
inch; what is its weight per foot ? 


SoLuTION.—By applying formula 151, the weight per foot is found 
to be .4418 k 3.4= 1.502 lb. Ans. 


NoTEe.—Some engineers prefer to estimate the weight of steel in the 
same manner as wrought iron and increase the result by 2 per cent. 
Thus, in the above example, the weight per foot of the bar, if of 


wrought iron, would be .4418 x = 1.473 1b., which, when increased 
by 2 per cent. equals 1.473 « 1.02 = 1.502 Ib., as above. 


EXAMPLE.—What is the sectional area given by two 6-inch channels, 
each weighing 8 lb. per foot, and a 10” « }" cover plate ? 


SoLuTIon.—The area given by the cover plate is 10” x #” = 2.50 sq. 
8X2 
3.4 
Therefore, the total area given by the section equals 2.50 + 4.71 = 7.21 

Sq.1ns) ANS. 





in. The area given by the two channels equals =q 4:71 sq. ih. 


880 PROPORTIONING THE MATERIAL. 


1487. The weight per foot of a round bar of steel may 
readily be obtained by applying the following convenient 


Rule.—Square the diameter of the bar, expressed in quarter 
aches, and divide by 6. 
This may also be expressed by the following formula: 


jigs - (153.) 


in which lV is the weight per foot of bar in pounds, and d is 
the diameter of the bar zz guarter inches. 


EXAMPLE.—What is the weight per foot of a round bar of steel 
8 inch in diameter ? 


SoLuTION.—Expressing the diameter of the bar in quarter inches 
9 
0 


and applying formula 153, the weight per foot is aS ia 1.50 lb. Ans. 





6 


ECCENTRICITY. POSITION OF PINS. BENDING 
STRESSES DUE TO WEIGHT OF MEMBER. 


1488. The bending moment upon a member under 
direct compressive stress, due to the weight of the member 
itself, should always be taken into consideration in fixing 
the positions of the pins. Some specifications also require 
the unit stress allowed upon the member to be reduced 
by the amount of stress per square inch required to resist this 
bending moment; or, what amounts to the same thing, re- 
quire the sectional area to be correspondingly increased. 
Many engineers, however, consider this latter to be an un- 
necessary degree of refinement for highway bridges. But 
it is very essential that the pins be placed as nearly as 
practicable in their proper positions. 


1489. Cooper's specifications contain the following: 


‘Tf the fiber strain resulting from the weight only of any 
membereexceeds ten per cent, of thes allowed junit strain 
on -stichy=member, “such” excess "musts be, consideredmam 
proportioning the areas.” 


1490. Zhe following are from Thacher’s specifications: 
‘‘For top chords, the stresses per square inch due to 


PROPORTIONING THE MATERIAL. 881 


weight of member will be deducted from the above unit 
stresses, the reduction for chords flat at one end being 
one-half, and for chords flat at both ends one-third the 
amount for members with pin ends. 

‘‘Unsymmetrical sections, composed of two rolled or 
riveted channels and one plate, shall in chords be so pro- 
portioned that the centers of pins shall be in the same line 
and in the centers of gravity of sections. In web members 
eccentricity .may be made sufficient to counteract the 
bending stress due to weight of member under maximum 
load.” 


1491. The following are from Lewts’s spectfications: 


‘““The effect of the weights of horizontal or inclined 
members in reducing their strength as columns must be 
provided for. It will also be considered in fixing the 
positions of pin centers. 

‘‘ All eccentricity of stress shall be avoided. Pin centers 
will be tin the center of gravity of the members, less the 
eccentricity required to provide for their own weight; and 
in continuous chords, pin centers must be in the same 
plane.”’ 

In these last specifications the conditions are very clearly 
stated, and the provisions there indicated will be quite 
fully noticed. Bending stresses in tension members, pro- 
duced by their own weight, are not usually provided for, 
as their only effect is to slightly increase the stress in the 
lower portion of the member. Furthermore, as the member 
deflects under its own weight, the bending stress becomes 
somewhat relieved by the deflection. But with a com- 
pression member the case is quite different. The bending 
moment produces eccentricity of stress; the effect of the 
bending stress combined with the direct stress is practically 
the same as that of an eccentric load upon a column, 1.e., it 
diminishes the efficiency of the member asa column. And 
this weakened condition is further augmented by the deflec- 
tion of the member due to its own weight. It is thus evident 
that the bending stress upon a compression member, due to 


882 PROPORTIONING THE MATERIAL. 


its own weight, materially impairs its strength and should 
be provided for. 


1492. The position of the center of gravity of a 
member is found by a process very similar to that explained 
in Art. 1373 for finding the center of gravity of a system 
of wheel loads. The position of a horizontal line passing 
through the center of gravity of a section may be readily 
found by applying the following 


Rule.—Wultiply the area (or weight) of each separate 
piece composing the section by the distance of its center of 
gravity from some given or assumed horizontal line, and 
divide the sum of the products by the sum of the arcas (or 
weights). The quotient will be the distance of the center of 
gravity of the entire section from the assumed line. 


Note.—The assumed horizontal line. from which distances are 
measured may be avy horizontal line, but should be preferably so 
situated that the center of gravity of each piece composing the section 
should be on the same side of the line. Thus, it is convenient to 
assume the line to pass through the center of the cover-plate, the top 
of the cover-plate, or the lower edge of the channels. All distances 
must be from the same line. 


EXAMPLE.—For the section of the upper chord given in Fig. 306 
(see also Mechanical Drawing Plate, Title: Highway Bridge: Details I, 
Fig. 1), find the distance of the center of gravity of the section below 
the tops of the channels. 








FIG. 307. 


SoLuTIoN.—The form of the section is shown in Fig. 307; the 
effective section is composed of two 8-inch channels weighing 10 pounds 
per foot and a 12” x 4” cover-plate. The sectional area of each channel 
is 19x ~,=3 sq. in., and that of the cover-plate is 12”x3?"=3 


PROPORTIONING THE MATERIAL. 883 


sq. in. If all distances be taken from a horizontal line through the 
center of the cover-plate, as xy in the figure, the distance of the center 
of gravity of the section from that line may be found by the following 
computation: 








Area Distance. 
Sc. 
CURT DIALE cain Ge sx tale tote 3.00 « 0.000 = 0.00 
db vorgelarsfet ett Roper La Ae ene ee 6.00 * 4.125 = 24.75 
9.00 24.75 
24.75 Te 
Hence, Ga 5 2.75 in. is the distance of the center of gravity of the 


section below the horizontal line xy through center of cover-plate. 
As this line is 4+ inch above the tops of the channels, the center ot 
gravity of the section is 2.75 — 0.125 = 2.625 in. below the tops of the 
channeis. Ans. 


In sections similar to the above, the distance from the 
center of gravity of the section to the center of the chan- 
nels or vertical plates is called the eccentricity of the 
section. Thus, the eccentricity of the above section is 
= — 2.625 = 1.375 inches. 

Tf a pin-connected member were subjected to direct longt- 
tudinal stress (tension or compression) only, the pins should 
pass exactly through its center of gravity. 

But, as a horizontal or inclined member is always sub- 
jected to a bending stress due to its own weight, this con- 
dition never fully obtains. As noticed above, it is seldom 
necessary to provide for the bending stress in a tension 
member, due to its own weight, and, consequently, the centers 
of the pins are usually located at the center of gravity of 
the member. But in a compression member the effect of 
the bending stress should be considered in fixing the positions 


of the pins. 


1493. Bending Moment on a Member Due to 
Its Own Weight.—Fig. 308 represents the entire upper 
chord, of which a section is shown in Fig. 307. The chord 
is shown in Mechanical Drawing Plates, Titles: High- 
way Bridge: Details I, and Highway Bridge: General 
Drawing. It will be noticed that in supporting its own 


884 PROPORTIONING THE MATERIAL. 


weight the chord acts as a beam continuous over two sup- 
ports. For compressive stresses some specifications consider 
each end panel of the upper chord as having one flat and 
one pin end, and all intermediate panels as having flat ends. 
For direct bending, the end panels are considered as beams 
having one end fixed and the other simply supported; and 
all intermediate panels as beams fixed at both ends. 














Fic. 308. 


In a uniformly loaded beam having one or both ends 
fixed, the greatest bending moment occurs at the fixed end. 
Formulas for the maximum bending moments in such beams 
are given in the Table of Bending Moments. As, however, 
the compression members of bridges resist principally direct 
compressive stress as columns, and as columns do not com- 
monly fail at the ends, but near the center, the bending 
moments at the ends may beneglected. It will, therefore, 
be necessary to consider only the maximum values of those 
bending moments which occur along the central portion of 
the member. . 

Neglecting, then, the bending moments at the ends, the 
greatest bending moment 47, which can occur along the 
central portion of a uniformly loaded beam fixed at both 
ends will occur at the center; its amount is given by the 
formula 


(154.) 


1494. The greatest bending moment J7, which can 
occur along the central portion of a uniformly loaded beam 
fixed at one end and simply supported at the other will 
occur at a distance of 2 /, from the free end; its amount is 
given by the formula 


9m ll, 
Ae neoshe 





iss) 


PROPORTIONING THE MATERIAL. 885 


1495. Ina uniformly loaded beam simply supported at 
both ends, the maximum bending moment J7 occurs at the 
center; its amount is given by the formula 


wll 
Ni Oo La 
8 


(156.) 

In all of the above formulas w is the load, or weight of 
member per unit of length, /, is the length of the beam or 
member, from center to center of supports or connections, 
and /, is the horizontal projection of Z,, which is usually 
simply the panel length. The unit of length must be the 
same for Z,as for w. It will be found most convenient to 
take w as the weight per foot of member and J/, as the 
length of member in feet. In order that the bending mo- 
ment shall be ininch-pounds, /, should be expressed in inches. 


1496. If the member is horizontal, then the distance /, 
will equal the distance /,. Calling 7, = 7/7, =/, formula1 56 
becomes ai 7 


Ma, 





(157.) 


which is the same as formula 7 of the Table of Bending 
Moments. 


1497. In applying any one of these formulas to obtain 
the bending moment in a built member, due to its own 
weight, the weight per foot, as estimated from the effective 
section, should be increased about 15 per cent. to provide 
for the weight of lattice bars, rivet heads, etc. 


EXAMPLE.—What is the bending moment in inch-pounds upon 
the end panel of the top chord designated in Fig. 306 and shown in 
Fig. 308 ? 

SoLuTION.—The sectional area of the chord has been found to be 
9 square inches; hence, the weight per foot of the effective section 
is 9 x= 30 lb., and the total weight per foot about 30+ .15 x 
30 = 34.5 lb. As this panel of the chord may be considered as a beam 
fixed at one end only, the bending moment is found by applying 
formula 155. In this case, w= 34.5, 7, =18, and 7, = 18 x 12; there- 
fore, the bending moment 

ox 54-01 x 1S OS 18 12 
AL, = —. 


138 = 9,431 in.-lb. Ans. 


886 PROPORTIONING THE MATERIAL. 


This bending moment is positive, and tends to produce 
compression in the upper portion of the chord and tension 
in the lower portion. It does not actually produce tension in 
any portion of the chord, because the direct compression 
in the chord, being much greater than the bending stress, 
entirely overcomes the tension, sq that the effect of the 
bending stress is really to increase the compression in the 
upper portion of the chord and diminish it in the lower 
portion. 


1498. The position of the pins may be so fixed that 
when the maximum direct compressive stress comes upon 
the chord, through the pins, it will produce an amount of 
bending moment equal to that produced by the weight of 
the member, but in the opposite direction (negative). 

This may be more clearly understood by reference to 
Fig. 309, which is a somewhat distorted representation, in 


Weight of Member 


a 


Center of Gravity ae 
















Applied 
Force 


_\€;_ Applied 
ee Force 


Fic. 309. 


outline, of the end-panel member of a top chord, indicating 
in a general way the relative positions of the forces. 

The two opposite bending moments will then balance 
each other, and the resultant stress will be direct compres- 
sion uniformly distributed over the section. Inthe ordinary 
form of upper chord and end-post sections, this condition 
will be effected when the position of the pins is fixed at 
a distance e, perpendicularly below the center of gravity of 
the section given by the formula 


ee 
ae, SA 
in which ¢, is the distance in inches below the center of 
gravity of the section at which pins should be fixed, J/ is 


a 


(158.) 


PROPORTIONING THE MATERIAL. 887 


the bending moment in inch-pounds due to the weight of 
the member, and S, is the total maximum direct compressive 
stress upon the member in pounds. 


1499. In fixing the positions of the pins in compression 
members in which the center of gravity of the section lies 
above the center, the total eccentricity, as previously 
obtained, must be reduced by the amount ¢,, which may 
be considered as negative eccentricity. The eccen- 
tricity, as thus reduced, is often called the final, or net 
eccentricity. 

EXAMPLE.—At what distance below the center of gravity should 
the positions of the pins be fixed in the end panel of the upper chord, 
Figs. 306 and 308, in order that the stress be evenly distributed over 
the section ? 


SOLUTION.—The bending moment due to the weight of the member 
has been found to be 9,431 inch-pounds = JZ. By reference to Fig. 306, 
the total amount of direct compressive stress upon the member is 
known to be 48,600 + 20,800 = 69,400 lb. = S.. Therefore, by applying 
formula 158, é, or the distance below the center of gravity of the 


9, 4¢ 
section at which the pins should be placed, is found to be Lach tee 


69,400 
186 in. Ans. 


EXAMPLE.—What is the net eccentricity of this section ? 


SOLUTION.—The total eccentricity of the section has been found to 
be 1.875 inches. ‘The eccentricity in the opposite direction due to the 
weight of the member, or the negative eccentricity, has been found 
to be .136 inch. Therefore, the net eccentricity is 1.3875 —.136= 
1.24in. Ans. 


1500. Increase of Section to Provide for Bend- 
ing Stress.—If in the above example the position of the 
pins be fixed at 1.24 inches, or practically 14 inches, above 
the center of the channels, the stress will presumably be dis- 
tributed uniformly over the section. But in proportioning 
' the material for this member, provision was made only for the 
direct compressive stress, while it has been shown that 
the member must also resist a bending stress due to its own 
weight. Therefore, the sectional area of the member 
should be increased an amount corresponding to the amount 
of this bending stress. As previously stated, this, by many 


888 PROPORTIONING THE MATERIAL. 


engineers, is considered an unnecessary degree of refine- 
ment in designing the members of highway bridges; but as 
some specifications require provision to be made for this 
condition, a method of determining the required increase of 
section will be explained. The method given below, though 
not in strict accord with some elaborate formulas which 
have been deduced for this purpose, is believed to give 
results sufficiently accurate for all practical purposes, and 
has the advantage of being very simple and easily applied. 

Formulas 72, Art, L241 ,and73, Art. Leas; civerie 
following values for the resisting moment, which must be 
equal to the bending moment: 


(159.) 


in which, as relating to the present case, J7 is the bending 
moment in inch-pounds, S may be the fiber stress per 
square inch or the assumed unit stress, A is the required or 
the assumed sectional area in square inches, 7 is the radius 
of gyration of the section in inches, and ¢ is the distance in 
inches from the neutral axis to the most remote fiber. 

In order to express the sectzonal arca required to resist the 
bending moment, formula 159 may be given the form 

Mc 
Am won (160.) 

By taking S to represent the allowed unit stress, and 
bearing in mind that the formula is applied after the general 
dimensions of the section are determined, it will be noticed 
that the values of all the quantities in the second term of 
formula 160 are known, and the value of A can be found 
by simply substituting these values. 

But some specifications require the fiber stress, produced 
by the bending moment, to be deducted from the allowed 
unit stress. To meet this requirement, a formula express- 
ing the amount of fiber stress per square inch may be 
derived from formula 159, as follows: 

Mc 
Pe ed 





Se (161.) 


PROPORTIONING THE MATERIAL. 889 


As the bending stress due to the weight of the member 
is always very small as compared with the direct compres- 
sive stress upon the member, the value of A as determined 
from the latter will be sufficiently accurate to use in 
formula 161. 

As previously stated, the bending moment tends to in- 
crease the compression in the uwffer portion of the section; 
hence, the stress in the extreme upper fiber becomes the 
critical stress, and, in applying the above formulas, the 
value taken forc should be the distance from the neutral 
axis to this fiber, or, in other words, the distance from the 
center of gravity of the section to the upper side of the 
cover-plate. 


EXAMPLE.—Referring to the examples previously given in this 
article, what is the sectional area required to provide for the bending 
stress upon the end panel of the upper chord, Figs. 306 and 308 ? 


SoLuTION. —The bending moment due to the weight of the member 
has been found to be 9,481 in.-lb. = JZ. ‘The distance from the center 
of gravity of the section to the top of the channels has been found to 
be 2.625 inches; hence, the distance from the center of gravity to the 
top of the cover plate is 2.625+ .25=2.875 in. =c. The bending 


quently, for the value of S in formula 160, the dead load unit stress 
should be used. By reference to Art. 1422, the dead load unit stress 
used for this section is known to be 14,600 lb. = S, and the radius of 
gyration of the section is 3.2in.=7. Therefore, by applying formula 
160, the sectional area required to resist the bending moment due to 
9,431 « 2.875 


the weight of the member is found to be 14,600 << 3.23 





eee Eo 7? att 
Ans. 
EXAMPLE.—For the same, what is the amount of stress per square 


inch of section produced by the bending moment, assuming the stress 
to be uniformly distributed over the entire section ? 





SoLuTION.—The same values are substituted in formula 161 that 
were substituted in formula 160 in the preceding example, except 
that the area of the section, as obtained for the direct compressive 
stresses, is used instead of the unit stress. The area of the section is 
9 square inches, and the stress per square inch required to resist 
the bending moment is found to be 


9,431 x 2.875 


9% 3.2? = 2941b. Ans. 


890 PROPORTIONING DHE MATERIAL: 


1501. In determining the final area of the section, 
the area required for the bending stress, as obtained by 
formula 160, may be added to the area required for the 
direct compressive stress; or, what amounts to the same 
thing, the stress per square inch required to resist the bend- 
ing moment, as determined by formula 161, may be 
deducted from the unit stress. 

The members of the bridge shown in Mechanical Drawing 
Plates, Titles: Highway Bridge: Details") IT sole Vein 
Highway Bridge: General Drawing, were proportioned 
according to Cooper’s specifications, which do not require 
that the bending stress upon a member due to its own 
weight shall be considered in proportioning the areas, 
unless it ‘‘ exceeds ten per cent. of the allowed unit strains 
on such member.” As the bending stress per square inch 
(294 lb.), determined above, does not exceed ten per cent. of 
the allowed dead load unit stress (.10 x 14,600 = 1,460 Ib.) 
it need not be considered in proportioning the area of the 
section. 


EXAMPLES FOR PRACTICE. 
1. In the end post shown in Mechanical Drawing Plate, Title: 


Highway Bridge: Details I, what is the distance of the center of grav- 
ity of the section above the lower edge of the channels? Ans. 5.84 in. 


2. What is the total eccentricity of this section ? Ans. 1.84 in. 


3. What is the bending moment upon this member due to its own 
weight, adding 15 per cent. for weight of details? Ans. 37,170 in.-lb. 


4. What is the ‘‘negative eccentricity,” or distance below the 
center of gravity, at which the pins should be fixed in order to coun- 
teract this bending moment ? Ans. .57 in. 


5. What is the net eccentricity of the section ? PS sid ae 


6. What is the sectional area required to resist the bending stress 
in the end post due to its own weight ? Ans. 1.39 sq. in: 
7. What is the fiber stress per square inch due to the same, if 
considered to be uniformly distributed over the entire section ? 
Ans. 781 1b. 
8. According to Cooper’s specifications, is it necessary to consider 
this fiber stress in proportioning the area of the section ? 


PROPORTIONING THE MATERIAL. 891 


GENERAL REMARKS. 


1502. The metal for the individual members of any 
truss bridge is proportioned in substantially the same man- 
ner as explained in the preceding articles for the example 
chosen to illustrate the process. Different specifications 
have somewhat different requirements, but the general 
methods of proportioning the material are much the same 
‘for all. When the operations explained in the foregoing 
pages are thoroughly understood, no difficulty will be ex- 
perienced in proportioning the material for a metal bridge 
according to any specifications. 


1503. The relative dimensions of the usual forms of 
chord sections are determined by formula 135, Art. 
1420. Post sections composed of two channels latticed, or 
of plates and angles latticed in the same general form, 
should comply with formula 129, Art. L414. All mod- 
ern compression formulas for wrought iron or steel columns 
make use of the radius of gyration; and for the forms of 
section shown in Fig. 303, this quantity is determined ap- 
proximately, but near enough for most practical purposes, 


by formulas 110 to 118, Art. 1408. 


1504. A tension member having a sectional area of 
more than about 3 square inches should consist of flat bars, 
which should always be placed in pairs. 

A wrought-iron tension member having a sectional area 
of less than about 2 square inches may consist of square or 
round bars, preferably the former. They should always be 
in pairs except when but one bar is used. A single bar 
used as a tension truss member should generally be a square 
bar. Round bars are commonly used for lateral rods. 

The thickness of flat bars used for tension members should 
always be between the limits of 4 and 4 of thetr width, and 
preferably between 4 and 1 of their width. 

The widths of flat bars should be multiples of a half inch; 
multiples of a quarter inch may be used, but are not desira- 
ble. The diameters of round bars and the sides of square 

I. II,—18 


892 PROPORTIONING THE MATERIAL. 


bars should generally be multiples of $ of an inch, though 
dimensions of sixteenths of an inch may be used. 


1505. In the selection of the material for metal bridges 
the following important considerations should be kept in 
mind: 


High steel ts not a suttable material to be used in bridges. 

Soft steel and medium steel are both superior to wrought 
tron for bridge purposes. 

For the riveted members of short span bridges, soft steel ts 
the best matertal. 

For all members of long span bridges, medium steel ts 
preferable, because it produces less dead load than soft steel 
or tron. 

lor forged eye-bars, medium steel ts the best matertal. 
Eye-bars forged of medium steel should afterwards be 
annealed. 

Medium steel ts the best material for pins. 

As steel 1s of nearly uniform strength tn all directions, it 
as the best matertal to be used for web-plates. 

All portions of the same built member should be of the 
same material, | 

Steel of a thickness greater than #, of an inch ts consider- 
ably injured by punching ; and, therefore, the use of greater 
thicknesses for riveted members should be avoided so far as 
possible. When greater thicknesses are used, the rivet holes 
should usually be punched Lof an inch smaller than required, 
and then reamed to the required diameter. Steel of a thick- 
ness greater than % of an inch should never be used without 
reaming. This refers to both soft and medium steel, but 
especially to the latter. 


1506. In proportioning the material for the members 
of a bridge, as well as in the calculations of stresses, unneces- 
sary exactness is to be avoided, as involving unnecessary 
waste of time. For the sake of explicitness, many of the 
computations in this Course have been made unnecessarily 
exact. 


PROPORTIONING THE MATERIAL. 893 


In general, it may be stated that unit stresses should be 
obtained correctly to the nearest ten pounds. Areas of 
sections should be computed and expressed to the nearest 
hundredths of a square inch, and the weights per foot of 
channels, angles, or other shape iron to the nearest tenths 
of a pound. 


1507. The student will find it to his advantage to 
closely observe and study the design of such metal bridges 
as may be situated in his vicinity, or as may come under 
his observation; he will thereby obtain many practical and 
valuable ideas of design, as well as a general knowledge of 
the usual practice. In doing this, however, he must bear 
in mind that the ordinary highway bridge does not always 
represent the best engineering practice, although it usually 
embodies principles of economical design. 

Railroad bridges, though possibly of less bold and eco- 
nomical design, will be found generally to represent better 
and safer engineering practice than highway bridges. 
Although the amount and distribution of the applied loads 
are different in the two classes of bridges, the frzuczples to 
be applied are the same for both. 





DETAILS OF CONSTRUCTION. 


GENERAL REQUIREMENTS. 


1508. Thus far in the study of Bridge Engineering, 
attention has been given solely to the general design. The 
designing of the details will now be considered. 

In America, metal bridges are manufactured at shops 
having special machinery and facilities for the purpose. 

Each individual member of a metal bridge, and some- 
times the entire bridge, if a small one, is manufactured 
complete at the shop. The various members of the struc- 
ture, as thus manufactured, are shipped to the bridge site, 
where they are placed in position and properly connected. 


1509. Before a bridge is manufactured, the practical 
constructive details of each member and its connections 
must be designed, and drawings must be made showing all 
such details. These drawings are known as detail draw- 
ings. When the bridge is designed by a consulting bridge 
engineer, complete detail drawings are usually made before 
the contract is let. But quite commonly, however, the 
drawings of the details are left to be made by the contract- 
ing company after the letting of the contract, the condi- 
tions for the details being usually covered by specifications. 
The latter practice is generally the more economical, as it 
allows the contracting company to use their customary 
details and such as are best suited to their equipment. But 
in every such case the drawings for the details should be 
submitted to, examined, and approved by the consulting 
engineer before any actual work on the structure is begun. 


1510: The drawings of the practical constructive 
details, from which the different portions of a bridge are 


For notice of copyright, see page immediately following the title page, 


896 DETAILS OF CONSTRUCTION: 


manufactured in the shop, are called shop, or working 
drawings. Each member of the bridge is manufactured 
strictly according to the shop drawings; the workmen are 
not allowed to vary from the drawings in any respect. 
Therefore, the shop drawings must not only represent good, 
practical, and workmanlike details and connections, but 
they must also be explicit in every particular, and absolutely 
accurate. 

Upon the shop drawings all distances and dimensions are 
plainly marked in figures, and, although the drawings are 
usually made to scale and the scale is marked upon them, 
dimensions are never taken by scale from the drawings. 
The dimensions as marked in figures govern in all cases. 
Dimensions less than two feet are marked in inches and 
halves, quarters, eighths, sixteenths, thirty-seconds, and 
sixty-fourths of an inch, although the last two fractions 
are seldom used. Decimal fractions are never used in 
shop drawings. Dimensions greater than two feet are 
marked in feet and inches, using fractions of inches where 
necessary. 

Any inaccuracy in the shop drawings will almost certainly 
result in a misfit between some parts of the structure. If 
discovered in the shop, the error can usually be corrected 
without very great expense or delay, but if not discovered 
until during the process of erection, the error will usually 
cause a large amount cf both delay and expense. Hence, 
the necessity of absolute accuracy in shop drawings can not 
be too strongly emphasized. This statement is made espe- 
cially pertinent by the fact that shop drawings are often 
required to be made hurriedly, so that the liability to error 
is great. 

The shop drawings of the highway bridge of 90 feet span, 
the design of which has been chosen to illustrate the prin- 
ciples given in the preceding articles, are shown in Mechan- 
ical Drawing Plates, Titles: Highway Bridge: Details I, 
II, III, IV, and Highway Bridge: General Drawing. 
The manner in which the dimensions of the same are deter- 
mined will now be studied. 


DETAILS’ OF CONSTRUCTION. 897 


SPECIFICATIONS. 


1511. As the structure referred to above has, with 
slight variation, been designed according to Cooper’s Gen- 
eral Specifications for Highway Bridges, such portions of 
these specifications as relate to the proportioning of the 
details are quoted below: 


(a,) Shearing and Bearing on Rivets.—‘‘ The rivets and 
bolts connecting the parts of any member must be so spaced 
that the shearing strain per square inch shall not exceed 
9,000 pounds, or ¢ of the allowed strain per square inch upon 
that member; nor the pressure upon the bearing surface 
per square inch of the projected semi-intrados (diameter Xx 
thickness of piece) of the rivet or bolt hole exceed 15,000 
pounds, or one and a half times the allowed strain per 
square inch upon that member. In the case of field rivet- 
ing, the above limits of shearing strain and pressure shall 
be reduced one-third part. Rivets must not be used in 
direct tension.” 


(0,) Shearing, Bearing, and bending on Pins.—‘‘ Pins 
shall be so proportioned that the shearing strain shall not 
exceed 9,000 pounds per square inch; nor the crushing strain 
upon the projected area of the semi-intrados of any member 
[other than forged eye-bars, see item (/,)] connected to the 
pin be greater per square inch than 15,000 pounds, or one 
and a half times the allowed strain per square inch; nor the 
bending strain exceed 18,000 pounds per square inch when 
the centers of bearings of the strained members are taken 
as the points of application of the strains.” 


(c,) Strength and Character of Detatls.—‘‘ All the con- 
nections and details of the several parts of the structures 
shall be of such strength that, upon testing, ruptures shall 
occur in the body of the members rather than in any of 
their details or connections. 

‘* Preference will be had for such details as shall be most 
accessible for inspection, cleaning, and painting; no closed 
sections will be allowed.” 


898 DETAILS OF CONSTRUCTION: 


(d,) ‘‘ The pitch of rivets* in all classes of work shall never 
exceed 6 inches, or sixteen times the thinnest outside plate, 
nor be less than three diameters of the rivet.” 

‘* The pitch of rivets at the ends of compression members 
shall not exceed four diameters of the rivets for a length 
equal to twice the width of the member.” 

‘‘The rivets used shall generally be 8, #, and ¢ inch 
CiamMevery me 

(¢,) ‘‘The distance between edge of any piece and the 
center of a rivet hole must never be less than 14 inches, 
except for bars less than 24 inches wide; when practicable 
it shall be at least two diameters of the rivet.” 


(7:)- “Wherever possible;-allwrivetemmine: pe tac 
driven. No hand-driven rivets exceeding {-inch diameter 
will be allowed. Field riveting must be reduced to a mini- 
mum or entirely avoided where possible.”’ 


(g¢,) Joints and Splices.—‘‘ All joints in riveted-tension 
members must be fully and symmetrically spliced.” 

‘‘In compression members, abutting joints with planed 
faces must be sufficiently spliced to maintain the parts accu- 
rately in contact against all tendencies to displacement.”’ 

‘“The ends of all square-ended members shall be planed 
smooth, and exactly square to the center line of strain.” 

‘‘In compression members, abutting joints with untooled 
faces must be fully spliced, as no reliance will be placed on 
such abutting joints. The abutting ends must, however, 
be dressed straight and true, so there will be no open joints.” 

‘“The sections of compression chords shall be connected 
at the abutting ends by splices sufficient to hold them truly 
in position.” 


(Z,) ‘‘Web plates of all girders must be arranged so as 
not to project beyond the faces of the flange angles, nor on 
the top to be more than ;, inch below the face of these 
angles, at any point.” 


* By the pitch of rivets is understood the distance from center 
to center of rivets in a line of rivets. In a long line of rivets the 
pitch is usually uniform. 


DETATES Ol CONSERUGLION. 899 


(z,) ‘‘In lattice girders, the web members must be 
double, and connect symmetrically to the web of the flanges.” 


(7,) ‘‘ The heads of eye-bars shall be so proportioned and 
made that the bars will preferably break in the body of 
the original bar rather than at any part of the head or neck. 
The form of the head and the mode of manufacture shall be 
subject to the approval of the engineer. The heads must be 
formed either by the process of upsetting and forging or by 
the process of upsetting, piling, and forging.”’ 


(4,) ‘‘ Zhe lower chord shall be packed as narrow as 
possible. 

‘““ The pins shall be turned straight and smooth, and shall 
fit the pin holes within ;4, of an inch for pins less than 
44 inches in diameter ; for pins of a larger diameter the 


clearance may be 3/5 inch.” 


(1) ‘‘ The diameter of the pin shall not be less than two- 
thirds the largest dimension of any tension member attached 
to it. The several members attaching to the pin shall be so 
packed as to produce the least bending moment upon the 
pin, and all vacant spaces must be filled with wrought-iron 
filling rings.” 


(7,) Upset Ends.—‘ All rods and hangers with screw 
ends shall be upset at the ends, so that the diameter at the 
bottom of the threads shall be ;4 inch larger than any part 
of the body of the bar. 

‘‘ All threads must be of the United States standard, 
except at the ends of the pins.” 


(z,) ‘‘floor-beam hangers shall be so placed that they 
‘can be readily examined at all times. When fitted with 
screw ends they shall be provided with check nuts. Pref 
erence will be given to hangers without screw ends. 

‘¢ When bent loops are used, they must fit perfectly around 
the pin throughout its semi-circumference.”’ 


(0,) Batten Plates and Lattice Bars.—‘‘ The open sides of 
all compression members shall be stayed by batten plates at 


900. DETAILS OF CONSTRUCTION. 


the ends and diagonal lattice work at intermediate points. 
The batten plates must be placed as near the ends as prac- 
ticable, and shall have a length of 14 times the width of the 
member. The size and spacing of the lattice bars shall be 
duly proportioned to the size of the member. They must 
not be less than 


14 XS GH LOL, scene dae 5 to 6 inch channels. 
13.2 NL CDAT ORS pee ee ees 7 to 8 inch channels. 
2. ein Ch tOrwe eee eee 9 to.12 inch channels. 
2b CCE ATICH LOle spencers 13 to 16 inch channels. 
a ap as ember el abs 8) phere Joa Way 17 to 20 inch channels. 
pee eee os Nal elas Heh Poppi Gneke 6 yar. 21 and upwards. 


‘¢ They shall be inclined at an angle of not less than 60° to 
the axis of the*member. ‘The pitch of the latticing must 
not exceed the width of the channel plus nine inches.” 


(~,) Reinforcing Plates.—‘‘ Where necessary, pin holes 
shall be reinforced by plates, so the allowed pressure on the 
pins shall not be exceeded. These reinforcing plates must 
contain enough rivets to transfer their proportion of the 
bearing pressure, and at least one plate on each side shall 
extend” not, less than six inches; beyond the edceromenrc 
batten plate.” 


(7,) forked tEnds.—‘‘ Where the ends of compression 
members are forked to connect to the pins, the aggregate 
compressive strength of these forked ends must equal the 
compressive strength of the body of the members ; in order 
to insure this result the aggregate sectional area of the forked 
ends, at any point between the inside edge of the pin hole, 
and six inches beyond the edge of the batten plate, shall be 
about double that of the body of the member.” 


(7,) ‘‘ Lhe attachment of the lateral system to the chords 
shall be thoroughly efficient. If connected to suspended 
floor-beams, the latter shall be stayed against all motion.” 


(s,) Portal Bracing and Transverse Diagonal Bracing.— 
‘All through bridges with top lateral bracing shall have 


DETAILS OF CONSTRUCTION. 901 


wrought-iron latticed portals, of approved design, at each 
end of the span, connected rigidly to the end posts. They 
shall be as deep as the specified head-room will allow. Knee 
braces shall also be placed at each intermediate panel point, 
and connected to the vertical posts and top lateral struts, 
for trusses 20 feet and less in depth. 

‘“When the height of the trusses exceeds 20 feet, an ap- 
proved system of overhead diagonal bracings shall be at- 
tached to each post at an elevation sufficient to give the 
required head-room, and to the top lateral struts.” 


(¢,) Expansion Rollers.—‘* All bridges over 75 feet span 
shall have at one end nests of turned friction rollers, formed 
of wrought iron or steel, running between planed surfaces. 
The rollers shall not be less than 2 inches diameter, and 
shall be so proportioned that the pressure per lineal inch of 
rollers shall not exceed the product of the square root of the 
diameter of the roller in inches multiplied by 500 pounds 
(500 /d@). 

‘‘ Bridges less than 75 feet span shall be secured at one 
end to the masonry, and the other end shall be free to move 
upon planed surfaces.”’ 


(w,) Anchors.—‘* While the roller ends of all trusses must 
be free to move longitudinally under changes of tempera- 
ture, they shall be anchored against lifting or moving 
sideways. 

‘* Variations in temperature, to the extent of 150 degrees 
(Fahrenheit) shall be provided for.”’ 


(v,) Led-Plates.—‘ All the bed-plates and bearings under 
fixed and movable ends must be fox-bolted to the masonry; 
for trusses, these bolts must not be less than 14 inches diam- 
eter; for plate and other girders, not lessthan ¢ inch diam- 
eter. The contractor must furnish all bolts, drill all holes, 
and set bolts to place with sulphur. 

‘* All bed-plates must be of such dimensions that the 
greatest pressure upon the masonry shall not exceed 250 Ib. 
per square inch.” 


902 DETAILS OF CONSTRUCTION, 


(w,) ‘All bolts must be of neat lengths, and shall have 
a washer under the heads, and nuts where in contact with 
wood.”’ 


(x,) Camber.—‘ All bridges with parallel chords shall be 
givena camber by making the panel lengths of the top chord 
longer than those of the bottom chord, in the proportion of 
73; of an inch to every 10 feet.” 


1512. In connection with the above items quoted from 
the specifications, the following important conditions will 
also be noticed: 


I. In chatn-riveting, the distance between the center lines of 
adjacent rows should preferably not be less than three diameters 
of the rivet, and in no case less than two and one-half diameters. 


Il. In zigzag, or staggered, riveting, the distance between 
the center lines of adjacent rows should preferably not be less 
than two and one-half diameters, and never less than two 
diameters. 


Ill. The distance from the center of the rivet hole to the 
edge of the plate (which should generally not be less than I+ 
anches) should in no case be less than one and one-half times 
the diameter of the hole for steel, nor less than one and five- 
erghths times the diameter of the hole for tron. 

Tf less than this, allowance must be made for the reduced 
strength of the joint. 


LV. The distance from the center of a rivet hole to the end 
of a wrought-iron plate (which should generally not be less 
than 14 inches) should in no case be less than one-half the 
diameter of the hole plus the thickness of the plate plus one-half 
anch. 

V. The grip of arivet, 2. ¢., tts length between heads when 
driven, should never exceed four times its diameter. 


VI. Countersunk rivets should not be used in plates of less 
thickness than one-half the diameter of the rivet. 


VIT. The heads of steel eye-bars should not be made thicker 
than the body of the bar. 


DETAILS OF CONSTRUCTION. 903 


1513. It will be expedient to explain here the respect- 
ive conditions distinguished by the terms szxgle shear and 
double shear, as applied to rivets. 

See Mechanical Drawing Plate, Title: Riveted Joints. It 
will be noticed that if the joint shown in Fig. 2, 3, or 4 should 
fail by shearing of the rivets, it would be necessary that each 
rivet should be sheared off but once; i. e., ‘cut once in two.” 
A rivet in this condition is said to be in singleshear. But 
in the joint shown in Fig. 5d or 6, it will be noticed that if the 
joint fails purely by shearing of the rivets, each rivet which 
fails must be sheared off twice; it must be sheared off between 
each two adjacent plates. The same would be true of the 
rivets in the joints shown in Figs. 7 and 8 when completed, 
and of those in the joint shown in Fig. 9. Rivets in such 
condition are said to be in double shear. It is evident 
that a rivet can not be in double shear unless it passes 
through more than two thicknesses of metal. 


Rule.—Rivets in double shear are allowed double the amount 
of shearing stress allowed upon the same size of rivets in single 
shear. 


CAMBER. 


1514. As actually constructed, the so-called horizontal 
chords of bridges are not made perfectly straight from end 
to end, but are curved slightly upwards, in order that when 
the truss is heavily loaded the chord will not be deflected 
below a horizontal line connecting its ends, which would 
give it the unpleasing appearance of sagging. This slight 
curve or crown given to the chords is called camber. In 
making the working drawings for a bridge, the first things 
to be determined are the amount of camber and the exact 
lengths of the members. , 

The camber of a truss is shown in an exaggerated manner 
in Fig. 310. It will be noticed that each panel of the lower 
chord is the chord of the arc of a circle, and that each panel 
of the upper chord is the chord of the arc of a somewhat 
larger circle having the same center. It is from this fact 
that the upper and lower longitudinal members of a truss 


904 DETAILS OF CONSTRUCTION. 


derive the name of chords: It will also be noticed that the 
vertical members are not truly vertical, but coincide with 
radii of the circle. 





FIG. 310. 


1515. What is spoken of as the amount of camber 
is the elevation of the center of the chord above its ends, 
i..e., the middle ordinate of the total arc, or the versed sine 
of the angle of one-half the arc. The amount of camber 
given to a bridge truss is usually from 1 to 2 inches for each 
100 feet length of span; that is, from 7545 to z+, of the 
span, although it may be more or less than these limits. 


1516. Inthrough bridges the camber is always obtained 
by increasing the length of the upper chord, the length of 
the lower chord remaining unaltered. The span length is 
practically unaffected by the camber; the slight curvature 
affects the length of the chord to such:a very small extent 
that it may be wholly neglected. 

In changing the form of the truss, the values of the stresses 
are also changed, but this change is very small and is 
entirely neglected. 

The amount z, which the length of each panel of the up- 
per chord is to be increased in order to give the required 


DETAILS OF CONSTRUCTION. 905 


amount of camber, is given approximately, but sufficiently 
close for all practical purposes, by the formula 


~=8er 
t= —_, 
NS 


(162.) 


in which ¢ is the amount of camber in inches, / is the height 
of truss in feet, s is the length of span in feet, and z is the 
number of panels in the truss. The value obtained for z is 
fi MIO ES 55 hc 

The definite amount of increase to be given to the upper 
chord, however, is commonly specified. In such cases the 
amount of camber may be obtained by substituting the value 
of zin formula 162, and solving for c. 


1517. According to item (7,) of Art. L511, the panel 
lengths of the top chord must be increased ,°, of an inch for 
each ten feet of length. In complying with this specifica- 
tion, some latitude must be taken in nearly every case, in 
order to avoid unusual and inconvenient fractions. For in- 
stance, in the truss of the example the panel length is 18 feet, 
and if the upper chord be increased 53, of an inch for each 

; 3 18; 27 
10 feet, the increase in each panel would be 18. 10> BO of 
an inch, which would be an inconvenient fraction to use. 
Increasing the panel length of the upper chord by 2 of an 
inch will be sufficiently close to the requirement of the 
specifications. 


EXACT LENGTH OF DIAGONAL MEMBERS. 

1518. By increasing the panel length of the upper 
chord, the lengths of all diagonal members also are increased ; 
this is shown in asomewhat exaggerated manner in Fig. 311. 
It will be noticed that the horizontal projection of each diag- 
onal member is increased by one-half the panel increase of the 
upper chord. Hence, the length d from center to center of 
the diagonal is given by the formula 


piae Vrs (+4). (163.) 


906 DETAILS OF, CONSTRUCAION: 


in which / is the height of the truss, f is the panel length, 
and zis the increase in a panel length of the upper chord, 
all in feet or all in inches. 

In applying the preceding formula, the operations may be 
somewhat facilitated by the use of logarithms, and still more 
by the use of a good table of squares. _Buchanan’s tables, 
giving the squares in feet for every foot, inch, and sixteenth 


Lefober Sn eee ryt eee ge 











FIG. 311. 


of an inch between one-sixteenth of an inch and fifty feet, 
are especially adapted to finding the lengths of truss diag- 
onals. In applying the formula without the aid of tables, it 
is usually expeditious to reduce all values to inches, or, in 
some cases, to convenient fractions of an inch. 


EXAMPLE.—In the truss shown in Mechanical Drawing Plates, 
Titles: Highway Bridge: Details I, H, III, IV, and Highway Bridge: 
General Drawing, the height of truss and panel length are each 18 feet, 
while the length of each panel of the upper chord is increased 2 of an 
inch for camber. What is the length of the diagonal, center to center ? 

a 
wise in. «Che 


panel length is the same. The panel increase 7 in the upper chord is 
: 3,459 - 
16 ; 


Formula 163 gives the center to center length of the diagonal = 
3,456? 8,459? 4,889.64 in. — 25’ 5 
Te ag tee ie 





SoLuTion.—The height of truss is 18 ft. = 216 in. = 


: z ‘ : Zz 
g of an inch, and 5 = 7 in.; hence, the expression +> = 
~ a 





" 


, very Closely. Ans. 





9 
2 


DETAILS OF CONSTRUCTION. ~ 907 


1519. The length of the diagonal, from center to cen- 
ter of fzus, will be taken at 25’ 542”, but in giving the length 
from center to center of pzz holes, allowance must be made 
for the clearance of pins. “ (See item (#,) of -Art. 1511.) 
For this purpose the clearance of each pin may be taken at 
sz of an inch. If the actual clearance is ;4 of an inch the 
error will not be of consequence. It is evident that when a 
member is under stress, the center of neither pin upon which 
it connects will coincide with the center of the pin hole, but 
one side of the pin will 
be in contact with the 
pin hole, while the op- 
posite side will be sepa- 
rated the full amount of 
the clearance. ‘This is 
clearly shown in Fig. 
pie. lf the clearance is 
zis of an inch, the center 
Sf the pin will be at a 






































—— > 
distance of 4X ay = 7, 
of an inch from the cen- 
ter of the pin hole. Ir FIG. 312. 


connected upon a ot ae each end, this tends to make a com- 
pression member ,*; = 3'y of an inch too short, and a tension 
member the same mrtitat too long. 


Rule.—lor all members connecting upon a pin at each end, 
the distance between centers of pin holes should be made 35 of 
an inch longer in a compression member, and in a tension 
member 5 of an inch shortcr, than tts calculated length. 


In pin-connected structures this applies to all diagonal 
and lower chord members, but not to upper chord members 
or vertical posts unless pin-connected at both ends. 

In the preceding example, therefore, the length of the end 
post, center to’center of pin holes, is 25’ 542” + 1,” = 25’ 58’: 
and the length of the ties, center to center of pin holes, is 
25' 543" — Ay" = 25' 5,".  Thelengthofa res chord mem- 
ber, center to’center of pin holes, is 18’ 0’ — +,” = 17' 1144". 


T. U1,—19 


905 DETAILS OF CONSTRUCTION. 


COMPRESSION MEMBERS. 


POSITIONS OF PINS IN CHORDS AND END 
POSTS. , 


1520. The next step in designing the details will be to 
fix the positions of the pins in the upper chord and end 
posts. As explained in Arts. 1498 and 1499, the eccen- 
tricity of the pins—that is, the distance of the centers of the 
pins from the centers of the channels—in a chord member or 
end post should be the same as the net eccentricity of the 
member. But it is evident that the pins should have the 
same relative positions throughout the chord and end posts. 
In the solutions explained in Art. 1499, the net eccentric- 
ity of the end panel of the upper chord was found to be 1.24 
inches; hence, the proper positions of the pins in this mem- 
ber would be at that distance above the centers of the 
channels. But in solving Example 5 of Art. 1501, the net 
eccentricity of the end post was found to be .77 of an inch, 
at which distance above the centers of the channels are the 
_proper positions of the pins in the end posts. 


1521. ln order to develop the full strength of a com- 
pression member, tt must be so connected that its resultant 
maximum stress will be distributed uniformly over its section. 

In properly designed bridges, therefore, the net eccen- 
tricity should be made the same throughout the entire 
upper chord and end posts. Had the chords and end posts 
of the example been properly designed, the weights of the 
channels in the upper chord would have been increased 
until the net eccentricity of this member became the same 
as in the end post. This would increase the sectional area 
of a member already having an excess of section, to which 
considerations of economy would offer some objection. The 
net eccentricity of the end post could have been made the 
same as the net eccentricity of the end panel of the upper 
chord without loss of economy, but the net eccentricity of 
the chord is too great to allow practical and consistent 
details. 


DETAILS OF CONSTRUCTION. 909 


In making general designs of highway bridges, it is 
frequently the case that the time available is not sufficient 
for determining sections having exactly the same net eccen- 
tricity. Consequently, conditions of eccentricity are often 
but loosely considered, and in many cases wholly neglected. 
In other cases, where time is limited, the designer depends 
upon his judgment to select sections having nearly the 
same eccentricity. If he is an experienced designer, he 
may be able to obtain reasonably approximate results; to 
do this is, at least, better practice than to neglect the 
eccentricity entirely. In the example, the top chord and 
end post sections have been proportioned to illustrate a case 
of this kind. 


1522. The designer of details is seldom the maker of 
the general design. The detailer must take the general 
design as it comes to him (in which, it is safe to say, the 
conditions of ideal perfection are seldom realized), and must 
from it evolve the best, and, at the same time, the most 
economical, structure possible. He must meet as best he 
can the conditions as he finds them. 

In a case similar to the example, having found that the 
net eccentricities of the chord and end post are not the 
same, the best thing to do is to make the eccentricity of 
the pins in those members a reasonable average between the 
net eccentricity of the end posts and the connecting or end 
_panels of the upper chord, and agreeing rather more nearly 
with the eccentricity of the end post. In the example, the 
net eccentricity of the end posts has been found to be .77 
in., and the eccentricity of the end panels of the upper chord 
1.24 inches. Hence, in this case, the pins in the top chord 


jeep eey a 
») i 


and end post are given an eccentricity of 1 





inch. An eccentricity of 13 of an inch would, perhaps, have 
been as good or even better. 

The positions of the pins, with reference to eccentricity, 
in the intermediate panels of the chord are not of great 
importance, unless the chord stresses are transmitted 


910 DETAILS OF CONSTRUCTION. 


through the pins, which is not usually the case. The pins 
are always given the same eccentricity throughout the upper 
chord. 


GENERAL DIMENSIONS OF THE UPPER CHORD 
AND END POST. 


1523. Sections of the channels used in the chords and 
end posts are shown in Fig. 79 of Mechanical Drawing. As 
there shown, the width of the flange in the 10-pound chan- 
nel (top chord) is 2;4 inches, while the width of the flange 
in the 16-pound channel (end post) is 2% inches. The 
latter channel has the wider flange, and as in the built 
member the flanges of the channels must not project beyond 
the edges of the cover-plate, the width of this flange will 
determine the distance between the channels of the end 
post, back to back. As two channels attach to the cover- 
plate, the distance back to back of the channels must not 
exceed 12 — 2 X 2,5, = 7#inches. Inmost cases it is best to 
allow each edge of the cover-plate to project about 54 of an 
inch beyond the flanges of the channels; but in the present 
case, as the channels of the end post, being much heavier 
than those of the upper chord, have flanges considerably 
wider than the channels of the upper chord, the flanges of 
the former channels are placed flush with the edges of the 
cover-plate. Hence, in the end-post the distance between 
channels, back to back, is made 72 inches. 

By. ‘reference’'to Pig. “17 -of “Mechanical” Drawing Viate, 
Title: Highway Bridge: Details I, it is noticed that on the 
end post the reinforcing pin plates for the hip joint & are 
placed inside the channels, and, in order to grasp the pin, 
extend beyond the channels of thesupper’ chord: in owe: 
that there shall be ;, of an inch clearance upon each side 
between these pin plates of the end post and the channels 
of the upper chord; the distance between the ‘latter, 
back to back, must be 7%-+ 2x ~,= 74 inches. As the 
pin plates must clear countersunk rivets, it would have 
been as well or better to have given 4 of an inch clearance 
on each side, but it would have produced greater bending 


DETAILS OF CONSTRUCTION. $11 


moment upon the pin. The width, out to out, of the flanges 
of the channels in the upper chord must not be greater 
Hianeerne swidtieofithe cover- plated -¢. 1 2cinches, “The 
width, out to out, of the flanges of the channels is found 
to be 74+ 2 X 2, = 11% inches, which is less than the 
width of the cover-plate. Sections of the top chord and 
end post are shown in Figs. 1 and 2 of the Mechanical . 
Drawing plate referred to above. 


‘ 


CLEARANCE. 


1524. It is very important that members which are 
to be connected in the field should have sufficient clearance, 
so that no difficulty will be experienced in making the con- 
nections. In this the designer must be governed largely by 
his judgment and the conditions of each individual case, 
but the following general rules indicate good practice, and 
will serve as a useful general guide: 


I. In arranging the several members upon a pin, pg of an 
wnch clearance should always be allowed between the connect- 
ing parts of adjacent members, tf eye-bar heads, forged loops, 
or perfectly smooth plates of a single thickness. 

IT, If the connecting portion of etther member consists of 
several thicknesses of perfectly smooth plates, from +5 to +5 
of an inch additional clearance should be allowed for each 
additional plate. 


Ill. If there are countersunk rivets in the connecting por- 
tion of either member, not less than} of an inch clearance 
should be allowed, the countersunk heads being also chipped. 


IV. If there are countersunk rivets in the connecting por- 
tions of both members, the countersunk heads being chipped, 
not less than =, of an inch clearance should be allowed. 

V. Lf the connecting portion of either member contains 
rivets with flattened heads or full heads, 4 of an inch clear- 
ance above the head should be allowed. 

VI. If the heads of countersunk rivets are not chipped, 

they should be considered as flattened to 4 of an inch, in estt- 
mating the clearance. 


912 DETAILS OF CONSTRUCTION. 


The clearance allowed between the connecting parts of 
members should always be ample; it should in no case be so 
scant as to cause squeezing or as to permit the possibility 
of the members not coming properly together. The pre- 
ceding rules apply to each clearance between the adjacent 
sides of members. 


SIZES OF PINS. 


1525. The stresses in the different members connect- 
ing upon a pin produce bending moment in the pin, the 
amount of which may be determined either by computation 
or by constructing the moment diagrams. According to 
itém ‘(b-) of Art TS 01. in “determining, toces leno a 
moment jwwpon a pin the centers of the. bearings 01, 116 
members under stress must be taken as the points of appli- 
cation of the forces. ‘The positions of the centers of the 
several bearings upon a pin depend to some extent upon 
their thickness, which in turn depends largely upon the size 
of the pin; for the required thickness of each bearing can not 
be determined until the size of the pin is known: ‘The con- 
ditions of bearing and bending being thus interdependent, 
it becomes necessary to assume certain dimensions and 
make trial calculations. It will be most expedient to assume 
a size for the pin. 


1526. Although the actual requirements are usually 
different for each pin, it is customary, in order to afford 
uniformity in the shop work, to make the pins of uniform 
diameter throughout the lower chord, including the shoe 
pin. It is evident, therefore, that the diameter of each pin 
in the chord must be equal to the diameter of the largest pin 
required inthe same. If the truss has an even number of 
panels, the largest pin required will almost invariably be the 
pin at the middle joint of the lower chord. If the truss has 
an odd number of panels, the largest pin will probably be 
required at the first or second joint from the center of the 
lower chord. After some experience, this can usually be 
determined by inspection. 


DETAILS OF CONSTRUCTION. 913 


When practical, the diameter of the hip pin is also made 
the same as the diameters of the lower chord pins. 

Item (/,) of Art. 1511 affords material guidance in as- 
suming the sizes of the pins in the lower chord. This item 
requires that, in the lower chord, ‘‘the diameter of the pin 
shall not be less than two-thirds the largest dimension of 
any tension member attached to it.” 

In the example, the member c c’ of the lower chord bears 
the greatest stress; it would be the largest member in the 
chord, were the chord composed entirely of chord bars, and 
it may, therefore, be considered as the largest tension member 
attaching to jointc. As actually designed, the width or 
largest dimension of the chord bar in this member is 44 inches, 
but of this width ;% of an inch is cut out by rivet holes 
and is not effective section. The width of the effective 
section is 44 — ;®% = 31% inches, or near enough for present 
purposes, 4 inches; this may be considered the largest dimen- 
sion of the chord bar. According to the requirements of the 
specifications, therefore, the diameter of the pin must not 
be less than ¢ X 4 = 2.67 inches = 2114 inches, nearly. 


1527. Ina truss having an even number of panels, the 
maximum bending moment J7 upon the pinat the center 
joint of the lower chord is given approximately, but quite 
closely, by the formula 

St 


Cs 9” 


(164.) 
in which S is the total live and dead load tensile stress in the 
adjacent panel of the chord and ¢ the average thickness of the 
heads of the chord bars connecting upon the pin plus {1 of an 
inch. This formula is necessarily applied before the dimen- 
sions of the chord bar heads have been determined, but if 
from the general conditions it is thought that it will be 
desirable to make the heads somewhat thicker than the body 
of the bar, allowance should be made for this fact in applying 
the formula. 

The formula may also be applied at the first or second lower 
chord joint from the center in a truss having an odd number 


914 DETAILS OF CONSTRUCTION. 


of panels, but the results are not so reliable. In such cases, 
S should represent the stresses in the adjacent panel towards 
the center of the truss. 

Having obtained the maximum bending moment, the size 
of the pin giving an equal resisting moment may be obtained 
from Table 40, Art. 1546, which will be further noticed in 
that article. 


1528. The total stressin the panel ce ofithe example 
(see stress sheet) is 48,600 + 20,800 = 69,400 pounds = S. 

The thickness of the head of each chord bar in the same 
panel is £ of an inch, and, consequently, the value of ¢ is 
$+ 4=+5 inch. Hence, by formula 164, the maximum 
bending moment upon the pin in the joint ¢ of the lower 
69,400 x 18 

2 

Item (0,) of Art, L511 requires that the bending sstress 
upon a pin shall not exceed 18,000 pounds per square inch. 
From Table 40, it isfound that, with a fiber stress of 18,000 
pounds per square inch, a bending moment of 32,500 inch- 
pounds will slightly exceed the resisting moment given by 
a 28" pin. 
As the bending moment obtained above is only approxi- 
mate, it will be well in choosing the diameter of the pin to 
select a diameter somewhat greater than the diameter thus 
obtained. Therefore, the diameters of all pins in the lower 
chord will be assumed to be 2% inches. With reference to 
the actual bending moment upon it, this diameter will now 
be investigated for the pin of the shoe joint. 





chord is, approximately, = 32,530 inch-pounds. 


PROPORTIONING PIN PLATES. 


1529. Shearing Upon Pin.—By the first condition 
of item (J,) of Art. 1511, the shearing stress per square 
inch upon the pin must not exceed 9,000 pounds. The total 
stress upon the end post is 45,800 + 19,600 = 65,400 pounds, 
one-half of which, or 32,700 pounds, is transmitted to the pin 
through each channel. Hence, the sectionalarea of the pin, 


DETAILS OF CONSTRUCTION. 915 


32,700 
9,000 
inches. The sectional area given by a pin or round bar 2? 
inches. in diameter is .7854 x 2.75" = 5.94 square inches. 
The shearing stress is found to be abundantly resisted by 


this size of pin. 


as required toresist the shear, is = oabe Square 


1530. Bearing Upon Pin and Thickness of Pin 
Plates.—The same item of the specifications requires that 
the crushing stress (bearing stress) per square inch upon 
the projected area of the semi-intrados (i. e., the diameter 
of the pin multiplied by the total thickness of metal bearing 
upon it, or, in other words, by so much of its length as is 
covered by the surface of the metal in the member bearing 
upon it) must not exceed 15,000 pounds, or one and one-half 
times the stress per square inch allowed upon the member. 

At 15,000 pounds per square inch, the allowed bearing 
upon one lineal inch of the pin is 15,000 X 22 = 41,250 
pounds, requiring for the total thickness of metal bear- 
45,800 +- 19,600 

41,250 





ing upon the pin = 1.59 inches, or a little 


less than 12 inches. 

In finding the value of the allowed bearing stress by ta- 
king one and one-half times the allowed stress per square 
inch, the reduction of the unit stress for length of column 
(i. e., the negative quantity in the compression formula) is 


; MS 
of course, neglected. Neglecting the quantity — 50 — in 


the compression formula, the live load unit stress allowed 
upon the end post is 8,750 pounds, and the dead load unit 
stress is 17,500 pounds [Art. 1410 (0)]. Hence, the bear- 
ing stresses allowed upon the pin are, for live load stress, 
8,750 x 14 = 13,125 pounds per square inch, and for dead 
load stress, 17,500 x 14 = 26,250 pounds per square inch. 
The bearing stresses allowed upon one lineal inch of the pin 
are, therefore, 13,125 x 22 = 36,090 pounds for live load 
stress, and 26,250 * 2% = 72,190 pounds for dead load stress. 
The required total thickness of metal bearing upon the pin 


916 DETALLS. OF CONSTRUCDION. 


45,800 19,600 
730, 000 ne, 190 
1,%, inches. Hence, it is found that the thickness of bearing 
required by the allowed bearing stress of 15,000 pounds per 
square inch asethe. greater. -/Dherefore, thesrequircamie a: 
thickness of bearing is 12 inches. 

It will be well to notice that, as the ratio between the live 
and dead load stresses is the same throughout the chord and 
end post, and as the unit stresses allowed upon the end 
post are less than those allowed upon the chord, it follows 
that the thickness of bearing required by the allowed bear- 
ing stress of 15,000 pounds per square inch will be greater 
than that required by one and one-half times the allowed 
stress, if applied to any portion of the chord or end post in 
this bridge; hence, the latter condition may be neglected 
and a bearing stress of 15,000 pounds per square inch used. 
This refers to the bearing stress either upon a rivet or upon 
a pin. 





is, then = 1.54 inches, or a little less than 


1531. When, as in the majority of cases, the allowed 
dead load unit stress is twice the allowed live load unit 
stress, the preceding operations are very much shortened by 
the following formulas: 


Let d = diameter of pin; 
az — allowed live load unit stress; 
2 uw = allowed dead load unit stress; 
L = total live load stress upon the member; 
L) = total dead load stress upon the member. 


Then, at 15,000 pounds per square inch, the allowed bear- 
ing stress per lineal inch of pin = 15,000 d@, and the required 
thickness ¢,, of metal is given by the formula 

L+D 
iz —_ 15,000 a” (1 65.) 

The values of 15,000 d@ are given in Table 40, Art. 1546. 
At 14 (= 3), the allowed unit stress for live load, the allowed 
bearing per lineal inch of pin = 3 x u x d, and the required 


DETAILS OF CONSTRUCTION. Oy 


seca hae 


ou > Saw 





Similarly, the 


D — 
BCE KB 


thickness for live load, ¢,= 





required thickness for dead load stress is 7, = 


fer Therefore, the total thickness 7 in this case is 
2L+ D 
bee Ter ts re ag (166.) 


In order to know what thickness should be provided for, 
we must compare ¢,, with 7, and take the larger. But, for 
this purpose, it is not necessary to compute both values; a 
general formula may be derived for the difference 7,,— 7. 
When this difference is positive, 7,, is greater than 7, and 
the value of 7,,, calculated by formula 165, should be used; 
when the difference is negative, the value of 7, calculated 
by formula 166, should be used. The formula for the dif- 
ference is found by subtracting formula 166 from formula 
165, which gives, after factoring, 


(7% — 5,000) D — (10,000 — w) LZ 


t.— —_ 
ees 15,000 du 





But, since the denominator does not alter the sign of the 
fraction, we may neglect it and write 


Siemon (tw re) 
sign of [(wu — 5,000) Y — (10,000 — w) L]. (167.) 


Therefore, formula 165 should be used when the second 
member of this equation is positive, and formula 166 when 
negative. Furthermore, by a simple process of factoring 
we may arrive at some very convenient formulas for the 
various cases likely to occur. Thus, in the preceding ex- 
ample, and zz all those of the same kind, we have u = 8,750. 
and formula 167 becomes 


sign of (t,,— T) = sign of (8,750 D — 1,250 L) = 
sign of [1,250 (3 D— L) = sign of (3 D—L)], 


whence the following 


918 DETAILS OF CONSTRUCTION. 


Rule.—for the bearing thickness of all posts [see Art. 
1410 (0)], use formula 165, tf three times the dead load 
stress excecds the live load stress. In the opposite case use 
formula 166. 


1532. For chord) seginents” [see Art TL Oat): 
wz — 10,000, and formula 167 gives 


sign of (¢,,— 1) = sign of 5,000 D, 
which 1s always positive. Hence, 


Rule.—Vor the bearing thickness of all chords in compres- 
ston, use formula 165. 


For other members to which the same rule applies, see 
Art. 1399 (gz). 

In all cases, formula 167 may be used to determine what 
thickness (whether ¢,, or 7) should be provided for; but it 
must be borne in mind that the preceding rules apply only to 
members proportioned by Cooper's specifications or by others 
containing the same requirements. 


1533. Referring to the section of the end post shown 
in Fig. 1 of Mechanical Drawing Plate, Title: Highway 
Bridge: Details I, it is found that the thickness of metal in 
the web of each channel of the end post is 2 of an inch. 
Hence, the thickness of bearing given by the two channels 
is 2X #= # of an inch, leaving 13 — ?= { of an inch thick- 
ness of bearing to be given by the two reinforcing pin plates; 
in other words, the two pin plates (one on each channel) are 
each required to be $ X $= +; of an inch in thickness. 

It is evident that this thickness, obtained for the pin 
plates, will apply not only to the shoe connection of the end 
post, but to the hip connection also, provided the same size 
pin is used. 


1534. Shearing Upon Rivets in Pin Plates.— 
If the stress is assumed to be distributed uniformly over the 
bearing surface, the amount of live load stress taken by each 
q's X 45,800 


pin plate is equal to 





= 12,330 pounds, and the 
“iat ale & 19,600 


amount of dead load stress is 4 iE = 5,280 pounds, 
8 


DETAILS OF CONSTRUCTION. ony 


or a total of 12,330 + 5,280 = 17,610 pounds. This amount 
of stress must be transferred from the channel to the pin 
plate by the rivets. 

According to item (@,) of Art. 1511, the shearing stress 
per square inch upon rivets must not exceed 9,000 pounds, 
or three-fourths of the allowed stress upon the member. 

The rivets used will be 2 of an inch in diameter, giving 
for each rivet a sectional area of (8)? x .7854 = .3068 of a 
square inch. An allowed shearing stress of 9,000 pounds 
per square inch will give 9,000 x .38068 = 2,760 pounds as 
the amount of shearing stress that may be allowed upon each 
rivet. Hence, the number of rivets required by this con- 
dition is eat = 6.4, or, as the result can not be fractional, 
7 rivets. 

Three-fourths of the live load unit stress allowed upon the 
end post is # X 8,750 = 6,560 pounds, and three-fourths of 
the dead load stress is # X 17,500 = 13,130 pounds. The 
amount of live load shearing stress allowed upon a rivet is 
6,560 X .38068 = 2,010 pounds, and the amount of dead load 
stress is 13,130 & .8068 =4,030 pounds. Hence, the number 





12,530 
of rivets required by the live load stress is 2010 = 6.1, and 
. 280 
the number required by the dead load stress is - z 030 wl BA 
) 


or, a total of 6.1+1.38= 7.4, or, as the result can not be 
fractional, 8 rivets. 

It may be noticed that, as applied to any portion of the 
end post of this bridge, the more severe requirement for 
shear is that the shearing stress per square inch shall not 
exceed three-fourths of the allowed stress upon the member. 


1535. When the allowed dead load unit stress is twice 
the allowed live load unit stress, we may use the following 
formulas, in which 7 is the total bearing thickness (13” in 
the moneding example), ¢= thickness of pin plate (,{," in the 
example), 4 = area of rivet, and w, D, and Z have aa same 
values asin Art. 1531. 


920 DETAILS OF CONSTRUCTION. 
Taking allowed shearing unit stress at 9,000 pounds, the 
required number of rivets is 


eet ee te) 
> 90004 I 





(168.) 


Taking allowed shearing unit stress at three-quarters unit 
stress allowed for members, the number of rivets is 


27(2L4 D) 
is eh la lay 


By subtracting 169 from 168 it is found that 


Sign of (n, —N)= sign of [(u — 6,000) D — (12,000 — wz) L] 
(170.) 


If this sign is p/us, use formula 1683 if mznus, use 169. 

Thus, in the preceding example, where uw = 8,750, 
(2 — 6,000) D — (12,000 — wu) L= 2,750 D— 3,250 L= 250 
(11 D—13 L) = 250 (11 x 19,600 — 13 x 45,000), which, 
being negative (this is seen at a glance without performing 
the operations) shows that /V is greater than z,, and that, 
therefore, formula 169 should be used for the number of 
TIVELS. 


Ve (169.) 


1536. Bearing Upon Rivets in Pin Plates.—The 
number of rivets required in the pin plate, when considered 
with reference to their capacity to resist bearing stress, will 
now be noticed. The thinnest plate through which the rivet 
passes is the web of the channel, which is practically 2 of an 
inch in thickness. As noticed above, the more severe re- 
quirement for bearing is that the allowed bearing stress shall 
not exceed 15,000 pounds per square inch. 

At 15,000 pounds per square inch, the bearing stress re- 
sisted by a 3” rivet through 2 of an inch thickness of plate, 
is X 2X 15,000 = 3,520 pounds. The number of rivets 
17,610 _ 
35520) ae 
5 rivets. Hence, at the unit stresses allowed for shearing 
and bearing, it is found that 8 rivets in each pin plate will 





required in each pin plate to resist the bearing is 


DETAILS OF CONSTRUCTION: 921 


fulfil all conditions for resisting the maximum stress 1n both 
shearing and bearing. 

The number of rivets required in each pin plate, as well 
as the thickness of the pin plate, isthe same for the hip con- 
nection of the end post as for the shoe connection. Eight 
rivets are used in each pin plate at the hip connection of the 
end post, but at the shoe connection, as six of the rivets are 
countersunk and four of them also flattened, ten rivets are 
used. In order to beon the safe side it is well to use one or 
two more rivets than the calculations require, especially if 
a number of the rivets are countersunk. 


1537. Tables of Shearing and Bearing Values 
for Rivets.—Operations similar to those explained above, 
for finding the number of rivets required in a pin plate and 
for like purposes, may be considerably facilitated by the use 
of the following tables of the shearing and bearing values of 
rivets. As allowed by many specifications, the unit value 
for bearing is double that allowed for shearing, and the tables 
are arranged accordingly. The values allowed by Cooper’s 
Highway Specifications, however, correspond with Table 37 
for bearing and Table 38 for shearing. Other unit values 
are used for both shearing and bearing, and other tables will 
be found in various structural hand-books, but the values 
given in these tables are those commonly used. According 
to the common practice, the values given in Table 36 are 
used for wrought iron in railroad bridges; those given in 
Tables 37 and 38 are used for wrought iron in highway 
bridges and for medium steel in railroad bridges; while the 
values given in Table 39 are used for medium steel in 
highway bridges. 

Nore.—In each table all bearing values above or to the right of the 
upper zigzag lines are greater than double shear. 

Between upper and lower zigzag lines bearing values are less than 
double shear and greater than single shear. 

Below and to the left of lower zigzag lines bearing values are less 
than single shear. 

All values in pounds. 

Shearing valuesat 12,000 pounds per square inch, and bearing values 


at 24,000 pounds per square inch may be obtained by doubling the 
values given in ‘lable 36. 







































































DETAILS OF CONSTRUCTION. 


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DETAILS OF CONSTRUCTION. 
















































































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924 DETAILS OF CONSTRUGCEION 


1538. Dimensions of Pin Plates and Arrange- 
ment of Rivets.—By reference to the sections of the chan- 
nels shown in Mechanical Drawing, Fig. 79, it will be noticed 
that the width of the widest plate that can be used upon the 
outside of the web of the channel of the end post (16 pounds), 
without rounding the edges to fit between the flanges of the 
channel, can not be greater than 8 — 2 (2+ +3) = 6¢ inches. 
Fitting the edges would involve additional and expensive 
shop work, and, therefore, should not be required when not 
absolutely necessary. Hence, pin plates 6 inches in width 
will be used upon the end post. The length of the pin plate 
will depend upon the number of rivets used and the arrange- 
ment of the rivet spacing. 

By item (¢,) of Art. 1511 the distance between the cen- 
ter cf -a rivet hole and the outer edge of the plate must not 
be less than 1} inches. If the outer lines of rivets in the 
pin plates be each located 14 inches from the outer edge of 
the plate, the distance between these two lines of rivets will 
be 6 — 2 X 14 = 34 inches; and if a row of rivets be placed 
midway between the two outer rows, the distance between 
two adjacent rows will be +x 34=1% inches. This is 
between two and one-half and three diameters of the rivets, 
and hence is a less distance between the rows of rivets than 
is desirable for chain riveting, but isa sufficient distance 
between the rows if the rivets are staggered. (Art. 1512, 
items II and III.) The rivets will be staggered, and their 
pitch will be made equal to twice the distance between the 
adjacent rows, or 34 inches. The distance from the center 
of any rivet hole to either the end. of the pin plate or the 
edge of the pin hole should not be less than 1} inches. The 
arrangement of the rivets in the pin plate to meet the required 
condition is clearly shown in Mechanical Drawing Plate, 
Title: Highway Bridge: Details I, Fig. 1. It will be noticed 
that with the rivets arranged as there shown, the shortest 
distance between the centers of any two rivets is the diag- 
onal distance between the centers of the rivets in two adja- 
cent rows; this distance is very nearly 24 inches, or four 
diameters. The arrangement of the rivet spacing in the 


DETAILS OF CONSTRUCTION. 925 


pin plate should usually be deferred until the size of the pin 
is definitely determined, and should always be worked out 
fully in pencil. Any change in the diameter of the pin 
would affect the required thickness of the material bearing 
upon it; it would, consequently, affect not only the thick- 
ness of the pin plate, but also the number of rivets in the 
same. 
MOMENTS ON PINS. 

1539. Positions of Bearings Upon the Pin.— 
‘The thickness of material necessary to give the proper bear- 
ing upon the pin, as required for the standards of the shoe 
and for the member in the end panel of the lower chord, will 
now be determined, in order to find the bending moment 
upon the pin. This is necessary because, according to item 
(6,) of the specifications (Art. 1511), the centers of the 
bearings of the members must be taken as the points of 
application of the stresses in determining the bending 
moment. 

The bearings of the shoe standards must be sufficient to 
resist the total vertical pressure upon them, which will be 
equal to the reaction due to the total wind pressure against 
the portal plus that due to the full live and dead loads. By 
reference to Fig. 277 (6) of Art. 1309, it will be noticed 
that the total wind pressure against the portal is equal to 
2,700 + 1,350 + 1,350 = 5,400 pounds. Hence, the vertical 
reaction at the foot of the leeward end post, due to this wind 
pressure against the portal, is equal to 5,400 x 4% = 5,116, 
or, near enough, 5,120 pounds. 

By reference to Arts. 1293 and 1301, it is found that 
the reaction due to a full live load is 32,400 pounds, and the 
reaction due to the dead load is 13,900 pounds. It has been 
found (Art. 1530) that for a bearing pressure of 15,000 
pounds per square inch the bearing value per lineal inch of 
a 22” pin is 41,250 pounds. Hence, the total thickness of 
bearing required in the standards of the shoe will be 
32,400 + 13,900 + 5,120 

41,250 
of + x 14}=3 inch for each standard. 


= 1.25 inches, which is a thickness 





> 


926 DETAILS OF: CONSTRUCTION: 


1540. The live and dead load stresses in the end panel 
a 6 of the lower chord are found to be the same as the live 
and dead load reactions. (This will always be the case for 
a full uniform load when the panel length and the height of 
truss at the hip vertical are equal.) Hence, for present 
purposes, the thickness of bearing of the lower chord upon 
the shoe pin may be considered the same as that taken for 
the shoe standards. 

The shoe joint may be arranged with the standards of 
the shoe between the channels of the end post and the lower 
chord members outside of the channels, but it is a better 
arrangement to pack the lower chord between the channels, 
with the shoe standards connecting outside of the end post. 
As the stress in the end post is resisted by both the stress 
in the lower chord and by the reaction, applied through the | 
shoe, the bearing of the. end post upon the pin should be 
between the bearing of the chord and the bearing of the 
shoe, as shown in Mechanical Drawing Plate, Title: High- 
way Bridge: Details IV. 

The distance between the channels of the end post, back 
to back, being 72% inches (Art. 1523), the distance from 
outside to outside of the pin plates at the shoe joint is 72 + 
2 (8-+ 7) = 9 inches. 

Rivets should not be flattened to less than + of an inch 
in height, and are always likely to be about one-sixteenth 
of an inch higher than marked. The shoe should have a 
clearance of not less than $ of.an inch on each side of the 
end post. Hence, the distance between the standards of 
the shoe is made equal to9+2(4+ + 4) = 94 inches. 
The distance from center to center of the pin bearings of 
the shoe standards is, therefore, 9§ + 8—104-inches. See 
Figs. 5 and 9 of Mechanical Drawing Plate, Title: Highway 
Bridges Detarlesii lL: 


1541. Asthe dimensions of the connecting details of 
the lower chord member a 6 have not yet been determined, 
the actual distance between the centers of their bearings, 
and, therefore, their actual positions with reference to the 


DETAIGS OF CONSTRUCTION. 927 


other bearings, are not known. Other conditions (to be 
hereafter noticed) may require the thickness of metal in the 
chord bearing upon the pin to be greater than required by 
the allowed bearing stress. In such cases it is good practice 
to assume the positions of the bearings to be the same as 
determined by the required thickness of bearing, with liberal 
allowance for clearance. Assuming the clearance on each 
side between the chord and end post to be }of an inch, 
the width from outside to outside of the chord connection 
will be 72 —2 x 4=“7tinches. If each bearing of the chord 
be assumed to be 2 of an inch in thickness, the same as the 
shoe standards, the distance between the centers of the 
chord bearings may be taken at 74 —%=64 inches. The 
distance between the centers of the bearings of the end 
post is known to be 73+ 2-+ 5; = 8,3, inches. 


1542. Bending Moment Upon the Pin.—The 
relative positions of the points of application of the forces 
acting upon the pin (which are the stresses in the connect- 
ing members transferred by the pin) have now been 
determined, and the maximum bending moment upon the 
_pin may be readily obtained. It isconvenient to resolve all 
forces acting upon the pin into their horizontal and verti- 
cal components, to determine the bending moments at vari- 
ous points in both the horizontal and vertical plane, and 
then find the resultants of the bending moments in the two 
perpendicular planes at corresponding points. The greatest 
of these resultants will be the maximum bending moment 
upon the pin. 

The forces acting upon the shoe joint, together with the 
force polygon for the same, are shown in Fig. 313. For 
each member the live and dead load stresses are combined; 
the wind stresses are neglected. A mere inspection of the 
force polygon clearly shows that 2-/, the vertical component 
of 3-7, the stress in the end post, is equaland opposed to the 
reaction 1-2; also, that 3-2, the horizontal component of 3-7, 
the stress in the end post, is equal and opposed to 2-3, the 
stress in the lower chord. Without performing any operation, 


928 DETAILS OF CONSTROUGTION, 


it is thus known that the horizontal component of the 
live and dead load stresses in the end post is equal to 46,500 
pounds, or the sum of the live and dead load stresses in the 
lower chord member with which it connects, and that the 
vertical component of the live and dead load stresses in the 
end post, which is equal to the reaction, is also equal to the 
same amount. The vertical forces acting upon the pin, and 
the horizontal forces acting upon the same, may each be 
considered independently of the other, giving very simple 


mm 
ty 


Seale of forces 1'-20000Ibs 





Z| 
Fic. 313. 


problems. The resultant of the two results may then be 
obtained, 


1543. In determining the actual bending moment upon 
a lower chord pin, the effect of the wind stress, though 
very often neglected, should be considered and provided for 
ina manner consistent with the method by which its effect 
upon the chord members connecting upon the pin was esti- 
mated in proportioning the material for those members. In 
other words, the bending moment upon the pin should be 
determined with regard to the effective sections of the mem- 
bers connecting upon it; a pin having an equal resisting 
moment would then be as strong as the connecting mein- 
bers. If the designer has not before him the data used in 


DETAILS OF CONSTRUCTION. 929 


determining the increase of area to provide for the wind 
load, he may proceed as follows: 

From the stress sheet he may take the dead and live load 
stresses (1) and L), divide them by the dead and live load 
unit stresses, respectively, as given by the specifications, and 
add the quotients. The result will be the area necessary for 
live and dead load stresses only. Call this area A. If the 
area given on the stress sheet is equal to A, this will show 
that no provision was made for wind stress, and the latter 
may be neglected in proportioning the pin. But, if the area 
A, given on the stress sheet is different from A, the amount 
WV of wind stress that must be provided for in dimensioning 
the pin is found by this simple proportion: 


L+D:A::L+D4+4W:A4,; 
whence, W=(L+D) (5 = 1). 


In the present case, the live and dead load unit stresses 
allowed are 10,000 and 20,000 pounds per square inch, re- 
spectively. From the stress sheet, the live and dead load 
stresses upon the lower chord member a @ are 32,400 and 
13,900 pounds, respectively, or a total of 32.400 + 13,900 = 
46,300 pounds. The sectional area required by the live and 
dead load stresses is tbe -- ica ala = 3.94 square inches. 

10,000 20,000 
As this is the area given on the stress sheet, no provision 
need be made for wind stress. 

At the shoe joint, the additional amount of stress assumed 
to provide for wind stress, when 4, is greater than A, may 
be considered to be resisted by the reaction, through the 
medium of the shoe. At each intermediate joint of the 
lower chord, if the lateral rods connect upon the floor-beams, 
and the latter connect upon the pins by means of hangers, 
this additional stress, assumed to provide for the effect of 
wind stress, may be considered to come upon the pin through 
the beam hanger and upon the chord through the pin. In 
other words, as the wind stresses are resisted by the lateral 
system, the additional stresses assumed to provide for the 


930 DETAILS OF CONSTRUCTION. 


effects of the wind stresses upon the lower chord may be con- 
sidered to come upon the chord through the piece by which 
the diagonals of the lower lateral system attach to the chord. 

This practice is not in all cases thoroughly consistent with 
accuracy, but the small error will probably be upon the side 
of safety. It is necessary to make some assumption by 
which the forces considered to act upon the pin will be in 
equilibrium. 


1544. The distance, as determined above, between the 
centers of the bearings of each member connecting upon the 
shoe pin, together with the stress upon the same, is givenin 
tabular form below. Stresses which act upwards or to the 
right upon the pin are designated by the + sign, and those 
which act downwards or to the left are designated by the — 


sign. Distance 


Horizontal 
Member: Between Vertical Stress, ce 
Bearings, Pounds. Dodade 
Inches. ese 
Shoe, 104 + 46,300 0,000 
End post, 833. — 46,300 — 46,300 
Lower chord, 64 0,000 + 46,300 


It will be noticed that in each column the sum of the 
stresses designated by the + sign equals the sum of the 
stresses designated by the — sign. 

The stress in each member is delivered upon the pin 
through two bearings, one-half of each stress through each 

ss bearing. The maximum bending 
| moment on the pin might be found 
by the force and moment diagrams; 





| 
8 but in a simple case like this it is 
3 ie easier to find it by direct calcula- 
3) is ~| tion. Fig. 314 shows one end of 
| ry §| the pin with the forces acting upon 
! | Q! 5 3 
38 Ze it.. /Dhe- distances, Detweengetwo 
| = "| consecutive bearing points is easily 
a 






determined from the distances tab- 


! 
Pastas & ulated above. Thus, distance from 
Fic. 314. & shoe bearing to center (middle) of 


DETAILS OF CONSTRUCTION. 931 


pin = 10} + 2 = 52’; distance from end post bearing to cen- 
ter of pin = 83, + 2 —4.9,". Therefore, distance between 
shoe bearing and end post bearing = 54 — ts = 42. The 
moment of the vertical forces = 23,150 X 3 = 26,770 inch- 
pounds. The moment of the horizontal forces = 23,150 xX 
24% = 19,530 inch-pounds. 

_ The resultant bending moment upon the pin is found by 
constructing a force polygon in the form 
of a right-angled triangle whose base 
and altitude represent, respectively, the 
horizontal and vertical bending moments 
as obtained. ‘The hypotenuse of the tri- 
angle will represent the resultant bend- 
ing moment upon the pin. This is clearly 
shown in Fig. 315. Or the resultant 
moment may be computed from the hori- 
zontal and vertical moments in the same Fic. 815. 
manner that the length of the hypotenuse is calculated in 
a right-angled triangle. It is equal to 4/26,770* + 19,530" = 
33,100 inch-pounds, nearly. 








1545. The Resisting Moments of Pins.—Having 
ascertained the maximum bending moment upon a pin, it is 
necessary to determine next the size of the pin required to 
resist the moment. The pin acts simply as a solid beam 
having a circular cross-section. 

The allowed bending stress, or stress per square inch upon 
the extreme fiber of pins (S, of formula 73, Art. 1243), 
commonly called the extreme fiber stress, is usually 
taken at 15,000 and 18,000 pounds for wrought iron, and 
at 20,000, 22,500, and 25,000 pounds for steel, according to 
the nature of the structure and the requirements of different 
specifications. For each material the lower unit values are 
used for railroad, and the higher unit values for highway 
bridges. 

Formula 73 is 7 

M=—, 


Cc 


in which J7 is the moment of resistance (which must be 


932 DETAILS OF CONSTRUCTION. 


equal to the bending moment), S is taken to represent the 
allowed stress in the outermost fiber (1. e., the extreme fiber 
stress), ¢ 1s the distance from the neutral axis to the outer- 
most fiber, and / is the moment of inertia of the cross-section 
of the pin. 

From the ninth item of Table of Moments of Inertia, it is 
3.1416 a* _ 

64 ~ 

-049 d*, and«c=4¢d¢ being the diameter of-the section, 

By substituting these values of / and c in the preceding 
formula, we get 


.049 S d* 
M = — id 


known that for a solid circular section / = 





— 098 Sda°. (171.) 


daairy lez ee} 


The values of J7 and d@ given by these formulas are suf- 
ficiently exact forall practical purposes. It is, however, much 
more expedient to obtain the values of J7 from a table 
prepared by formula 171. 


1546. Table 40 gives the values of the resisting mo- 
ments of pins for each eighth of an inch from 1 to 5§ inches 
diameter, for fiber stresses of 15,000, 18,000, 20,000, 22,500, 
and 25,000 pounds. For convenience, the bearing values 
for 1 anch. thickness ‘of “plate.(—‘dianieter sof spingcslen 
allowed bearing stress per sq. in.) are also given for bearing 
stresses of 12,000, 15,000, and 18,000 pounds per square inch. 

For the resisting moments of pins having diameters ex- 
pressed in odd sixteenths of an inch, it will be sufficiently 
correct to use a value 50 pounds less than a mean between 
the next lower and next higher values. Thus, with a fiber 
stress of 15,000 pounds per square inch, the resisting moment 
19,700 + 23,000 


of a 2,'," pin may be taken at 5 


— 50 = 21,300 


inch-pounds. 
For intermediate bearing values, a mean between the next 
lower and next higher values may be taken. 


DETAILS OF CONSTRUCTION. 


TABLE 40. 


BEARING VALUES AND RESISTING MOMENTS OF PINS. 








Diameter of 
Pin in Inches. 

































































Bearing Values, in 
Pounds, for One Inch 


















































933 





Moments, in Inch-Pounds, for Extreme 



































































































































ge Thickness of Plate. Fiber Stresses of 
a an ae 
: ’ 15,00 18,0 5300 8,000 9, 95° 2594 
ae Seg Ib. pee Ib. wee lb per i. per Ib. per tb. per 1b. er its er 
“|Square|Square| Square | Square | Square | Square | Square | Square 
Inenh va Ine he _ Inch. _ Inch, Inch. Inch. Inch. | Inch. 
0. 785| I2,00C} I5,000| 18,000} 1,470} 1,770] 1,960} 2,2I0} 2,450 
0.994} 13,500} 16,900] 20,300) 2,100] 2,520] 2,800] . 3,140} 3,500 
I.227| 15,000] 18,800] 22,500} 2,880} 3,450) 3,830] 4,310} 4,790 
1.485| 16,50C} 20,600] 24,800] 3,830} 4,590] 5,100] 5,740} 6,380 
1.767| 18,000] 22,500} 27,000] 4,970] 5,960} 6,630! 7,460} 8,280 
2.074| 19,500] 24,400} 29,300] 6,320} 7,580) 8,430) 9,480] 10,500 
2.405| 21,000] 26,300] 31,500} 7,890} 9,470] 10,500] 11,800) 13,200 
2.761| 22,500] 28,100} 33,800} 9,710] 11,600] 12,g00| 14,600] 16,200 
3.142] 24,000] 30,000} 36,000] 11,800} 14,100] 15,700} 17,700] I9,600 
3.547| 25,500] 31,900} 38,300] 14,100] 17,000] 18,800] 21,200} 23,600 
3.976] 27,000] 33,800] 40,500} 16,800] 20,100] 22,400] 25,200] 28,000 
4.430| 28,500] 35,600) 42,800] 19,700} 23,700} 26,300] 29,600} 32,900 
4-909} 30,000} 37,500] 45,000} 23,000] 27,C00o| 30,700] 34,500) 38,400 
5.412| 31,500] 39,400} 47,300} 26,600) 32,000} 35,500) 40,000) 44,400 
5.940) 33,000} 41,300} 49,500) 30,600} 36,800) 40,800) 45,900, 51,000 
6.492) 34,500) 43,100) 51,800} 35,000) 42,000) 46,700) 52,500) 58,300 
7.069} 36,000) 45,000} 54,000] 39,800) 47,700} 53,000} 59,600} 66,300 
7.670) 37,500} 46,900) 56,300! 44,900} 53,900) 59,900) 67,400) 74,g00 
8.296} 39,000} 48,800} 58,500} 50,600) 60,700) 67,400) 75,800) 84,300 
8.946] 40,500} 50,600] 60,800) 56,600) 67,g00) 75,500) 84,900) 94,400 
94 9 ] 9 9 
g.621| 42,000) 52,500] 63,000] 63,100) 75,800) 84,200) g4,700| 105,200 
10. 321| 43,500] 54,400} 65,300) 70,100, 84,200) 93,500] 105,200) 116,900 
I1.045) 45,000] 56,300) 67,500] 77,700) 93,200} 103,500) 116,500] 129,400 
II. 793] 46,5ccC| 58,100} 69,800) 85,700] 102, 80c} 114,200} 128, 500; 142,800 
12.566} 48,00C| 60,000} 72,000} 94,200] 113, 10C | 125,700] 141,400] 157, 100 
13.364] 49,500] 61,900) 74,300} 103,400) 124,000} 137,800) 155,000) 172,300 
14.186) 51,000] 63,800) 76,500] 113,000) 135, 700] 150,700) 169,600) 188,400 
15.033] 52,50C| 65,600) 78,800} 123,300} 148,000] 164, 400] 185,000} 205,500 
15.904} 54,00C|] 67,500) 81,0CO} 134,200) 161,000] 178,g00} 201, 300} 223, 700 
16.800] 55,500] 69,400) 83,300] 145, 700) 174,800} 194,300} 218, 500) 242,800 
17.721] 57,000] 71,300) 85,50C} 157,800) 189,400] 210, 400} 236, 700| 263,000 
18.665] 58,50C| 73,100) 87,800] 170,600) 204, 700} 227, 500] 255,g00| 284,400 
19.635} 60,00C}.75,000} 9g0,00C) 184, 100} 220, g0C} 245,400] 276, 100) 306, 800 
20.629] 61,500] 76,g00} 92,300} 198, 200} 237,900} 204, 300| 297, 300} 330,400 
21.648] 63,000] 78,800} 94,500) 213,100] 255,700) 284, 100) 319,600) 355,200 
22.691| 64,500] 80,600} 96,800} 228, 700) 274,400} 304,900} 343,000) 381, 100 
23.758) 66,000} 82,500] 99,000} 245,000} 294,000] 326, 700] 367,500} 408, 300 
24.850] 67,500] 84,400} LOL, 300} 262, 100} 314, 500} 349, 500} 393, 100) 436, 800 
25.967| 69,000] 86, 300} 103, 500} 280,000] 335,900] 373,300) 41g,g00, 466,600 
27.109] 70, 50C| 88, 100} 105, 800| 298,600} 358, 300} 398, 200] 4.47, 900| 497, 700 











934 DETAILS OF CONSTRUCTION. 


In the present structure, according to item (0,) of the 
specifications (Art. 1511), the bending stress must not 
exceed 18,000 pounds per square inch. 

By reference to Table 40, Art. 1546, it is found that 
with an extreme fiber stress of 18,000 pounds per square inch, 
a pin 2% inches in diameter has a resisting moment of 36,800 
inch-pounds. 

Hence, this diameter of pin will resist the bending moment 
upon the shoe pin, which has been found to be 33,100 inch- 
pounds. It may be noticed that, at 18,000 pounds per square 
inch, the resisting moment given bya2}{ 4" pin is practically 
32,000 + 36,800 
ee 
have been sufficient to resist the bending moment. 


50 = 34,350 inch-pounds, which would 


PIN PLATES FOR THE HIP JOINT OF THE 
CHORD. 


1547. Thickness of Bearings for Chord.—The 
total maximum stress upon the upper chord is 48,600 + 
20,800 = 69,400 pounds. From Table 40 it is found that, at 
15,000 pounds per square inch, the bearing value for one 
inch thickness of metal upon a 2?” pin is 41,300 pounds. 

The total thickness of bearing surface upon the pin re- 
69,400 
41,300 
inches, or, practically, 144 inches. By reference to Fig. 79 
of Mechanical Drawing, it is found that the thickness of 
web in the upper chord channel (10 lb. per ft.) is 34 of an 
inch, or a total thickness of 51, of an inch for both channels; 
leaving 141 — 54 = 14 inches thickness of bearing to be 
given by the two pin plates, or 2 of an inch each. 


quired for the stress in the upper chord is =="10.68 





1548. Pin Plates.—It is desirable that the pin plates 
should extend beyond and around the pin, Hence, as the 
pin plates at the upper end of the end post are on the 
inside of the channels, the pin plates of the chord must be 
upon the outside. The width from outside to outside of the 
webs of the channels of the chord is 74 + 2 X 35 = 743 inches, 


DETAILS OF CONSTRUCTION. 935 


while the corresponding width from outside to outside of 
the webs of the channels of the end post is 72+2x2= 8} 
inches. This will not allow the pin plates directly on the 
outside of the webs of the channels of the chord to extend 
beyond the pin, outside of the webs of the channels of the 
end post. It will, therefore, be necessary to make the pin 
plates on the chord double, extending only the outer plates 
beyond and around the pin. Two pin plates, each ;'; of an 
inch thick, instead of one plate 2 of an inch thick, will be 
placed upon the outside of the web of each channel of each 
chord, and the outer plate only will extend beyond and 
around the pin. 

As determined above, the total thickness of bearing 
required for the chord is 1.68 inches, and the thickness 
given by the pin plates is 1.25 inches. Hence, the amount 
of live load stress to be transferred to the pin plates by the 
rivets is 48,600 x be = 36,160 pounds, and the amount of 


dead load stress to be transferred by the same is 20,800 X 
1.25 | 
L687 15,480 pounds, or a total of 36,160 + 15,480 = 51,640 


pounds. 





1549. Rivets Required by Shearing Stress. — 
Neglecting the reduction for column length, the live and 
dead load unit stresses allowed upon the upper chord: are 
10,000 and 20,000 pounds, respectively. Three-quarters of 
the live load unit stress (see item (@,) of Art. 1511) is 
7,500 pounds, and from Table 37, Art. 1537, the value of 
a §" rivet in single shear at 7,500 pounds per square inch 
is 2,800 pounds, while for dead load stress it will be double 


this amount, or 4,600 pounds. Hence, the number of rivets 








area : eso, 1G 
required in the pin plates by this condition is aes 
} DUL 
8 ‘ 
15,480 0 = 19.1, or, as the result can not be fractional, 20 
4,600 
rivets. 


At 9,000 pounds per square inch, the value of a 8” rivet 
in single shear is 2,760 pounds (Table 38, Art. 1537), and 


936 DETAILS OF)CONSTRUCTION, 


the total number of rivets required in the pin plates by this 
36,160 + 15,480 _ 
CRON AN in | 
1550. Rivets Required by Bearing Stress. —The 
thinnest plate through which the rivets pass is the web of 
the channel, which is slightly less than }” in thickness. At 
15,000 pounds per square inch, the bearing value of a 
8” rivet in }” thickness of plate is 2,340 pounds. (Table 
37, Art. 1537.) Using this value, the total number of 
36,160 + 15,480 
2,340 
rivets. The bearing is found to be the critical condition. 
The required number of rivets as found is for the pin 
plates upon both channels; the number required in the pin 


G)s 


z =, 11 rivets: As the 


pin plates on each channel are double and the separate 
plates are of equal thickness, one-half of this number of 
rivets will be required for each plate. All the rivets neces- 
sarily pass through the inner plate, but only half of them, or 
6 rivets, are required in the outer plate. The arrangement 
of the rivets in the pin plates of the chord is very similar to 
the arrangement in the pin plates of the end post, and will 
require no special explanation. These pin plates will be 
noticed again. 


condition is 





18.7%, or, practically, 19 rivets. 


=) 





Tivets “required gins the. pln ep ateese 


plates attaching to each channel is 





MOMENTS ON HIP PIN. 

1551. Positions and Intensities of Bearings 
Upon Pin.—The thickness of the bearing upon the hip pin 
for each channel of the upper chord, including the pin plates 
upon it, being assumed equal to ++ 5, + 4% = # inch, the 
distance from center to center of the two bearings of the 
upper chord upon the hip pin is equal to 74+ $= 82 inches. 
At the hip joint, the distance between the inner surfaces of 
the pin plates of the end post is 72 — 2 x +, = 6} inches, and 
the distance from center to center of the two bearing sur- 
faces of the end post upon the hip pin is 644+ 7,+2=7 
inches. The main tie bars and hip vertical rods are both 





DETAILS OF CONSTRUCTION. 937 


packed inside, or between the bearings of the end post. As 
the main tie bars bear greater stress than the hip vertical 
rods, the former are packed adjacent to the end post bear- 
ings. The thickness of the tie bar is 1% of an inch, but on 
account of the pin being situated so near to the tops of the 
channel, thus limiting the diameter of the head of the tie 
bar, it is very probable that it will be found necessary to 
thicken the heads of the tie bars, in order to give sufficient 
metal back of the pin hole. Hence, in obtaining the bend- 
ing moment, it will be well to consider the tie bar heads to 
be £ of an inch thick. 

Allowing }” clearance on each side, the distance between 
the outer sides of the heads of the tie bars is 64 —2 x ¢=6} 
inches, and the distance from center to center of this 
bearing surface is 64—$=52 inches. The clear dis- 
tance between the inner surfaces of the tie-bar heads is 
64—2 xX $= 44 inches. 

A clearance of one-sixtecenth of an inch ts all that ts neces- 
sary to allow between two eve-bar heads, or between an eye- 
bar head and a welded loop. (See Art, 1524, 1.) 

Hence, the distance from outside to outside of the loops 
of the hip vertical rods will be 44 — 2 x 44 = 42 inches, and, 
as the hip vertical rods are 1 inch square, the distance from 
center to center of the same is 42 — 1 = 32 inches. 

The stress in the upper chord is horizontal, and equal to 
69,400 pounds. 

The stress upon the hip vertical is vertical, and equal to 
20,800 pounds. 

The stress in the end post has a horizontal and a vertical 
component, each of which has been found to be equal to 
46,300 pounds. (Art. 1542.) 

It is evident that the greatest bending moment upon the 
pin will occur with the truss fully loaded, as this condition 
will give the maximum stress to every member connecting 
upon the pin except the main tie 4¢. The stress upon the 
main tie with the truss fully loaded, not being the maximum 
stress upon that member, is not shown upon the stress sheet. 
But it is evident that, in order that the forces acting upon 


938 DETAILS OF CONSTRUCTION. 


the hip joint shall be in equilibrium, the horizontal compo- 
nents of the stresses of the main tie and end post must be 
equal to the horizontal stress in the upper chord, as no other 
stress having a horizontal component. acts upon this joint. 
Hence, the horizontal component of the stress in the main 
tie is equal to 69,400 — 46,300 = 23,100 pounds. Similarly, 
its vertical component must be equal to the vertical com- 
ponent of the stress in the end post minus the stress in the 
hip vertical and the one-third panel dead load (2,300 pounds) 
assumed to be supported directly at the hip joint, or 46,300 — 
(20,800 + 2,300) = 23,200 pounds. As the vertical and hori- 
zontal projections of the tie (height of truss and panel 
length) are equal, the vertical and horizontal components of 
its stress are found to be practically equal; they are really 
exactly equal. 

The one-third panel load of dead load (2,300 pounds) 
assumed to be applied directly at the hip joint may be con- 
sidered to come upon the pin through the bearings of the 
upper chord. 

The distance between the centers of the two bearings of 
each member connecting upon the pin, together with the 
horizontal and vertical stress upon the same, as determined 
above, is given in tabular form below. 

Those stresses which act upwards, or to the left, upon the 
pin are designated by the + sign, and those stresses which 
act downwards, or to the right, are designated by the — 
sign, 


Distance : 
Beveeen Horizontal : 
Member. Rieecs Vertical Stress, 
Bearings, Pp rs Pounds. 
Inches. Fea 
Upper chord, 88 + 69,400 — 2,300 
End post, (ous — 46,300 + 46,300 
Main tie, 5# — 23,100 — 23,200 
Hip vertical, 3g 0,000 — 20,800 


. 


In each column the sum of the stresses designated by the 
+ sign equals the sum of the stresses designated by the — 
sign. 


DETAILS OF CONSTROCTION. 939 


1552. Bending Moments Upon Pin.—The force dia- 
gram and equilibrium polygon for the horizontal forces 
acting upon the pin are shown at (a) in Fig. 316, and at (0) 
in the same figure are shown the force diagram and equilib- 
rium polygon for the vertical forces. 

For the horizontal forces the pole distance is 40,000 
pounds. The maximum intercept, uniform from ¢ d, is, to 
scale, .74 of an inch. Hence, the maximum horizontal 
bending moment is 40,000 x .74 = 29,600 inch-pounds. 

For the vertical forces the pole distance is 30,000 pounds, 
and the maximum intercept, uniform from @ tog, is, toscale, 
1.04inches. Hence, the maximum vertical bending moment 
is 30,000 * 1.04 = 31,200 inch-pounds. 

The resultant maximum bending moment is equal to 


VW 29,6007 + 31,2007 = 43,000 inch-pounds. 


1553. Resisting Moment of Pin.—For a bending 
stress of 18,000 pounds per square inch, as allowed for 
wrought iron by item (0,) of the specifications (Art. 1511), 
this amount of bending moment would require a pin 3 inches 
indiameter. But on account of the pin being located so 
near the top of the channels, it would be very undesirable to 
use a pin having a diameter greater than 2? inches. Hence, 
as all the conditions except the bending moment are satisfied 
with a 2?” pin, it will be better, instead of using a larger size 
of pin, to use a 23” pin of medium steel. 

Cooper’s specifications do not directly state the intensity 
of bending stressallowed upon pins of medium steel. But, 
as they allow upon medium steel in the main members of 
a bridge unit stresses 20 per cent. greater than those allowed 
upon wrought iron, we may assume the same ratio of increase 
in the bending stresses to be allowed upon the pins. At 
18,000 pounds per square inch, the resisting moment of a 2?” 
pin is 36,800 pounds. (See Table 40, Art. 1546.) 

An increase of 20 per cent. would give a resisting moment 
of 1.20 K 36,800 = 44,200 inch-pounds, which ts sufficient to 
resist the bending moment of 43,000 pounds, as obtained 
above. 

T. [1.—21 


DETAILS OF CONSTRUCTION. 


940 





Tiorizontal Forces 














_ a i a i ig a a a a ee Re Ce ee ee ae a eee ee ee ee eee ee 


To 
' 


” 


4 


Scale of distance 2 


mw 


(D) 


Scale of forces 1 




















S 
S 
Ss 
= 
s 
bs 
Sy 





DETAILS OF CONSTRUCTION. 941 


It will be noticed that for this size of pin a bending stress 
of 22,500 pounds per square inch, which is sometimes used 
for pins of medium steel, will give a resisting moment of 
45,900 inch-pounds. 


CONSTRUCTIVE DETAILS OF THE END POST. 


1554. The dimensions of the connecting details of the 
end posts having been determined, the constructive details 
and rivet spacing for that member, with the exception of the 
connections for the portal bracing, may now be determined 
and laid out. These should be drawn out entirely in pencil, 
as it may afterwards become necessary to modify certain 
dimensions slightly, in order to provide for the conditions of 
connecting members. The details of the end posts are 
shown in Mechanical Drawing Plate, Title: Highway 
Bridge: Details I, Fig. -1. 


1555. The Top View; Positions of Rivet Lines. 
—The first step with reference to the rivet spacing is to fix 
the positions of the two lines of rivets connect- 
ing the cover-plate to the channels. The dis- - 
tance between these two lines of rivets is 
governed by the distance a, Fig. 317, from the 
center of the rivet hole through the flange of 
the channel to the back of the same, together 
with the distance, back to back, between the two 
channels. 

As the widths of the flanges of the same size 
channels vary considerably, not only as rolled 
in different mills, but also as rolled in different 
weights in the same mill, it is impossible to fix 
a general standard for the distance from the 
back of the channel to the rivet holes through _ 
the flange. The following formula, however, = F!6 31% 
gives values for this spacing which are sufficiently close for 


practice: a 
ice 8 4 a3 (1 73.) 





in which ais the distance from the back of the channel to 


942 DETAILS OF CONSTRUCTION. 


the center of the rivet hole for the minimum weight of 
channel, and d isthe depth of the channel, both in inches. 
peerio ole 

For channels heavier than the minimum weight, but of 
the same form, except with thicker web (i. e., in which the 
weight is increased by simply spreading the rolls), the space 
a should be increased by the amount a, as derived by the 
following formula: 

ge (174) 

in which zw, is the zzcrease in pounds of the weight per foot 
above the minimum weight, and d is the depth of channel, as 
above. 

The value given to the space a, Fig. 317, should contain 
no fraction smaller than one-sixteenth of an inch. , 


1556. It may here be noticed, incidentally, that from 
formula 174 may be obtained the thickness of the web or 
the width of the flange of a channel of any weight, when the 
thickness of web or the width of flange in the minimum 
weight of the same size and form of channelis known. In 
this formula, a, equals the increase in the thickness of web, or 
width of flange, for cach pound per foot increase in weight. 

This formula gives accurate results for wrought iron only. 

The values of the spacing given by formula 173 will, in 
many cases, vary slightly from the standards adopted by 
various manufacturers. Each large manufacturer of struc- 
tural material usually has his own standard spacing, suited 
to the widths of the flanges in the channels manufactured 
by him. | 

Perhaps the most notable exception to the correct appli- 
cation of formula 173 occurs in the case of light 8” channels. 
As rolled by some mills, the lighter weights of this size of 
channels (10 pounds per foot) have flanges no wider than the 
ordinary widths of flanges in 7” channels. The spacing for 
the flanges of these lighter weights of 8” channels will here 
be obtained by applying formula 173 the same as for 9’ 
channels. When the weight of the channel does not greatly 


DETAIES OF. CONST RUGRION;: 943 


exceed the minimum weight, formula 174 need not be 
applied. 

Thus, in the example, for the 8” channels of the upper 
chord, the space a should equal } x 7++4= 14 inches. 
Hence, as the distance between the channels, back to back, 
is 7$inches (Art. 1523), the perpendicular distance between 
the rows of rivets connecting the cover-plate to the channels 
in the upper chord is 74+ 2 X 14=9#% inches. This dis- 
tance should usually be made the same on the chord and end 
post. The distance, back to back, between the channels of the 
end post is 72 inches. Hence, the distance a, from the center 
of the rivet hole through the flange to the back of the 


9% — 7% 
channel, will be made equal to ea; = 1, inches. _ This 


spacing is shown on the top view of the end post, Mechani- 
cal Drawing Plate, Title: Highway Bridge: Details I, 
Fig. 1. If the channels of the end post were of lighter 
weight, having narrower flanges, the distance between the 
backs of the channels, and also between the rivet lines, 
would be somewhat greater. The positions of the rivet 
dines being thus fixed, the spacing of the rivets is readily 
laid out. 





1557. Spacing of Rivets in Cover-Plate.—By 
item (d,) of the specifications the pitch of the rivets must 
not exceed 6 inches, or sixteen times the thickness of the 
thinnest outside plate. The cover-plate in the end post is 
8 of an inch thick; hence, the pitch of the rivets connecting 
it to the channels must not exceed 16 X 2=6 inches. The 
maximum pitch of the rivets in the cover-plate has been 
made 5 inches, though, in compliance with the specifications, 
it could have been 6 inches. Near the ends of the member 
the pitch of the rivets should always be materially dimin- 
ished; and, so far as possible, the rivet spacing should be 
the same at both ends of the member; that is, the rivet 
spacing on the two halves of the member should be sym- 
metrical with reference to the center (between pin holes) of 
the member. This facilitates the laying out of the werk in 


944 DETAILS OR CONSTRUCTION, 


the shop. The sum of the rivet spaces between the centers 
of the pin holes should be exactly equal to the length of the 
member between those points. ‘Thus, in the end post of 
the example, the sum of the rivet spaces between centers 
of pin holes is as follows: 


53 spaces at Sie TO CNes ean 
2 spaces at 4-9. inches =. 0’ 93” 
4 spaces at AY itiches ela 
2 spaces at Sa ACheS— et) ci 
2 spaces 3 and 14+ inches= 0’ 4?’ 
2 spaces 24 and2 inches= 0’ 4}” 





Distance center to center of pins = 25’ 58” 


At the lower end of the end post, the rivet spacing 
between the center of the pin hole and the end of the mem- 
ber should exactly correspond with the length between those 
two points. At the top of the end post, the rivet spacing 
must correspond with the holes left vacant for connecting 
the hip cover-plate, which in this case serves also as a 
connection for the portal bracing. 

The bevel for the hip joint should be carefully determined 
by laying out in pencil, to a large scale, the general dimen- 
sions of a side elevation of a hip joint somewhat similar to 
the side elevation shown in Mechanical Drawing Plate 
Title: Highway Bridge: Details IV, Fig. 13; and the exact 
bevel should be shown on the side elevation by the base and 
altitude of a right-angled triangle, one of which dimensions 
should be 12 inches for convenience in laying out in the 
shop. The exact length of both cover-plate and channels 
should be given. 


1558. The Bottom View; Batten Plates.—For 
the details of the bottom view, the positions of the batten 
plates (sometimes also called tie plates and stay plates) 
are first approximately determined. Theyshould be as near 
to the ends of the member as possible, but should give ample 
clearance for the members connecting upon the pins. The 
position of the lower batten plate, giving sufficient clearance 


DETAILS OF CONSTRUCTION. 945 


for the lower chord member, may be found by drawing 
accurately in pencil a side elevation of the shoe joint simi- 
lar to that shown in Fig. 17 of the plate just referred to, 
but omitting unnecessary portions. From thisdrawing may 
also be determined the general dimensions of the standards 
of the shoe; also, how much, if any, of the lower corners of 
the channels of the end post it will be necessary to cut off, 
and how far back from the end it will be necessary to cut 
away a portion of the lower flanges of the channel, in order 
that the end post will fit into the shoe with sufficient clear- 
ance, as shown on the side elevation and bottom view in 
Fig. 1, same title as above, I. 

The position of the upper batten plate on the end post, 
giving sufficient clearance for the hip vertical rods, may be 
found by drawing the hip vertical rods in their proper posi- 
tion in the side elevation of the hip joint drawn to determine 
the bevel. From this drawing may also be obtained the 
position of the batten plate on the upper chord, giving 
sufficient clearance for the main tie bars. 


1559. Inarranging the approximate position of each 
batten plate, a clearance of about one inch should be given 
to the member connecting upon the pin. According toitem 
(0,) of the specifications, each batten plate must have a 
length equal to 14 times the width of the member, or, in the 
present case, 14 x 12=18 inches. The thickness of the 
batten plates should be not less than ;4, of the distance 


o 


between the rivet lines in the parts which the batten plates 
Ky 
ie 


, Pie 
Colnect, or, in the present. case, i .195 of an inch. 


a 


© 


The thickness of the batten plates, however, may generally 
be the same as the thickness specified for the lattice bars on 
the same member, or, in this case, + of an inch. According 
to the first condition of item (d@,) of the specifications, the 
pitch of the rivets in the batten plates of the example 
must not exceed 16 X }=4 inches. By placing each of the 
outer rivets in the batten plate at a distance of 14 inches 
from the corresponding end of the plate, there will remain 


946 DETAILS OF CONSTRUCTION. 


18 — 2 x 14 = 15} inches’ between these rivets, which may 
15.5 
ee 
distance between the rivet lines on the lower side of the end 
post is the same as the corresponding distance on the upper 
side, or 9# inches. 


be divided into four spaces of = 3f inches each. The 


1560. _ It will be well to notice also that item (d,) of the 
specifications requires that ‘‘the pitch of rivets at the ends 
of the compression members shall not exceed four diameters 
of the rivet for a. length equal to twice the. width ofthe 
member.” As the batten plate usually comes within this 
length, the pitch of rivets in it should be considered to be 
governed by this condition, although this was not done in 
the example. In any case, however, the following is a safe 


Rule.—J/n chords and end posts, make the pitch of rivets 
wn the batten plates as nearly as practical the same as in that 
portion of the cover-plate directly opposite. This pitch, how- 
ever, must in no case excecd sixteen times the thickness of the 
batten plate. 


1561. The Lattice Bars.—The portions of the bot- 
tom flanges of the channels of the end post situated between 
the batten plates are to be stayed by diagonal bars, called 
lattice bars.’ When the diagonal stays or braces of this 
system do not intersect each other at any point between 
their ends, as is the case on the chord and end post of the 
example, the system is sometimes called lacing, and the 
bars are called lacing bars, those bars only which cross 
each other being called lattice bars. In this Course, how- 
ever, the distinction will not be made, but all such systems 
of stays or bracings will be designated as lattice, and the 
bars as lattice bars. 


1562. Lattice bars connected by one rivet at each end, 
as in the present case, should have a width of about three 
times the diameter of the rivet used, or, in our example, 
about 3X 3=1f inches. Item (0,) of the specifications 
(Art. 1511) requires the size of lattice bars used to connect 


DETAILS OF CONSTRUCTION. 947 


the flanges of 8” channels to be 12” x }’.. The same item 
specifies that the lattice bars shall be inclined at an angle 
of not less than 60 degrees with the axis (center line) of the 
member. ‘The distance between the batten plates may be 
divided into any number of equal spaces that will give the 
required pitch. In order that the pitch of the lattice bars 
may not contain an inconvenient fraction, the spacing may 
be started from the inner rivets of the batten plates, as 
shown in Mechanical Drawing Plate, Title: Highway 
Bridge: Details I, Fig. 1, or it may begin at points on the 
channels about 24 inches from those rivets, a distance just 
sufficient for the lattice bar to clear the batten plate. It is 
better practice to have the lattice bars connect upon the 
inner rivets of the batten plates. The positions of the bat- 
ten plates may be slightly changed to suit the spacing of the 
lattice bars. It must be remembered that the rivets attach- 
ing the lattice bars to one channel are midway between 
those attaching them to the opposite channel, requiring half 
spaces at the ends, which may both come upon the same 
channel and count as a whole space, or one may come upon 
each channel and thus count as a half space. 


1563. The exact length / of the lattice bars, from cen- 
ter to center of rivet holes, should always be given; it may 
be found by the following formula: 


f= v (2) + w?, (175.) 


in which 7 is the pitch of the lattice, 1. e., the distance be- 
tween two adjacent rivets connecting the lattice bars in the 
same rivet line, and w is the perpendicular distance between 
the two rivet lines. 

If the lattice bars are inclined at an angle of exactly 60 
degrees, 


pa) eee. (177. ©) 


Thus, in the end post of the example, if the inclination of 
the lattice bars is 60 degrees, the pitch of the lattice is equal 
to the length of the bars = 1.1547 x 9.75 = 11.2583 inches, 


948 DETAILS OF CONSTRUCTION: 


or, practically, 114 inches. It is found that by taking ad- 
114 
pi 
is made, to count upon each channel at the opposite ends of 
the latticed length of the member, the bottom plates can 
readily be so arranged that a pitch of 114 inches can be used. 


vantage of the half space of = 52 inches, one of which 


1564. The distance of the outer rivet in each batten 
plate from the center of the pin hole should be given. 
These two distances, together with the rivet spacing on the 
batten plates and the spacing for the lattice bars, when 
added together, must give the exact length of the member 
from center to center of pin holes. On the end post of the 
example these distances are as follows: 


1 space at 12%inches= 1’ 02’ 
4 spaces at 38finches= 1’ 3}’ 
22 spaces at 114 inches = 20’ 74" 
dspace. at Seunches =. o. 


4 spaces at 3finches= 1’ 33’ 
lspace at 8%inches= 0’ 83’ 


Distance center to center of pins = 25’ 53” 


DETAILS OF THE UPPER CHORD. 


1565. The arrangement of the constructive details of 
the upper chord is so very similar to that for the end post 
as to require very little special explanation. The thickness 
of bearing and number of rivets required, determining the 
sizes of the pin plates upon the chord at the hip, were found 
in connection with the details of the hip joint. In the cover 
plate, the pitch of rivets must not exceed 16 x 4 = 4 inches. 
In the greater portion of the length of the member the pitch 
of the rivets is 4 inches, but it is reduced towards the ends 
of the member. Near each end of the panel the rivet 
spacing is necessarily accommodated to the details of the 
connecting members. Between the centers of the pin holes 
the sum of the rivet spaces exactly equals the panel length. 

On top of the cover plates is riveted the bent plate for 


DETAILS OF CONSTRUCTION. 949 


connecting the portal bracing and also the short pieces of 
augles forming the lateral connections. The intermediate 
lateral strut also connects on top of the chord at C, vacant 
holes for this connection being shown in the cover-plate and 
cover splice plate. 


1566. The lateral connections are placed as near to 
the portal and intermediate struts as practicable, but allowing 
sufficient clearance. The angles at which the lateral con- 
nections or lateral hitches are placed upon the chord are 
determined by the positions of the points at which the cen- 
ter lines of the lateral rods intersect the center line of the 
chord. Each point of intersection is also the center, in 
each direction, between the rivets connecting the short 
pieces of angles forming the lateral connections, or, in other 
words, the center of the lateral hitch. Theoretically, these 
points, where the center lines of the lateral rods intersect 
the center line of the chord, should be at the intersections 
of the center lines of the lateral struts with the center line of 
the chord. It is impossible, however, to locate the lateral 
hitches at these intersections, but they should be located as 
near to them as possible. 

At the hip joint, the distance from the center of the pin 
to the center of the lateral hitch is 14,3, inches, and at the 
intermediate joint C, the distance between the center of the 
pin and the lateral hitch of the end panel is 8,3, inches. 
Hence, as the panel length of the chord is 18’ 02", the 
longitudinal projection of the lateral rods in the panel 2 C, 
from center to center of connections, i. e., the distance be- 
tween the centers of the two lateral hitches, is 18’ 02” — 
(14,3," + 8,3,") = 16’ 2" =194 inches. The lateral projection 
of the lateral rods, center to center of connections, 1. e., the 
distance from center to center of chords, is 18 + 1 = 19 feet = 
228 inches. In determining the base and altitude of the 
right-angled triangles which show the angles of the lateral 
hitches, if the smaller dimension be made 12 inches, by 
calling the greater dimension x, we have the proportion 
194 ; 228 :: 12: 4, whence x = 14.103, or slightly more than 


950 DETAILS OF CONSTRUCTION. 


14.3, inches. For the convenience of the workmen, one of 
these dimensions should always be 12 inches. 


1567. Splice Plates and Intermediate Joint.— 
The channels and cover-plate of the upper chord are spliced 
as near the joint at C as is practicable for the details of the 
connecting members. The ends of the channels and cover- 
plates are to be planed to give true abutting surfaces. Ac- 
cording to item (g,) of the specifications, the joint must be 
spliced sufficiently to maintain these parts accurately in con- 
tact. A splice plate is placed on top of the cover-plate and 
on the outside of the web of each channel. Sometimes, in 
large chords, small angle bar splices are also placed on the 
lower sides of the lower flanges of the channels, but it was 
not done in this case. The splice plates on the outsides of 
the webs of the channels serve also as reinforcing plates for 
the pin bearings, as do also the plates for the post connec- 
tion on the insides of the channels, really giving con- 
siderably more than the required amount of bearing for the 
pin. 

As the splice plates for the channels and cover-plate of 
the chord do not bear stress, but simply serve to hold the 
parts in position, no rule can be given for calculating the 
number of rivets required. ‘The designer must be guided 
by his judgment and by such conditions as may arise in 
each individual case, always endeavoring to make a neat 
and substantial joint. Sufficient clearance should always be 
given between the heads of rivets passing through the web 
of the channel and the heads of rivets passing through the 
flanges of the same. 

The bending moment upon the pin at this joint is pro- 
duced wholly by the stress upon the counter rods ; it occurs 
in the plane of these rods, and is found by a single moment 
diagram. It will not be necessary to explain the process in 
detail. 


1568. Batten Plates and Lattice Bars.—The size 
of the batten plates, as well as the size of the lattice bars, is’ 
the same on the chord as on the end post. The position of 





DETAILS OF CONSTRUCTION. 951 


the batten plate near the hip joint must be such as to give 
sufficient clearance for the main tie bars, which is deter- 
mined by a drawing of the side elevation of the hip joint, as 
previously stated. The batten plate in the end panel near 
the intermediate joint C is not required to clear any diagonal 
member, but it should be as near the splice as practicable. 
It is found that by carefully arranging the positions of the 
batten plates, the pitch and, consequently, the length of the 
lattice bars on the chord can be made the same as on the end 
post. The pitch of the lattice bars throughout the chord 
and end posts should be made the same where practicable. 
The rivet spacing on the bottom of the chord between centers 
of the pin holes should add up exactly equal to the panel 
length. 

All rivet spacing in the center panel of the chord is made 
as nearly the same as that of the end panels as the condi- 
tions will permit. ‘The position of the batten plate, giving 
sufficient clearance for the counter rods, is determined by 
drawing a side elevation of the intermediate joint similar to 
that shown in Mechanical Drawing Plate, Title: Highway 
Bridge: Details IV, Fig. 14. As this panel of the chord is 
made perfectly symmetrical with reference to the center of 
the panel, only one end need be shown. 


CONSTRUCTIVE DETAILS OF THE INTERME- 
DIATE POST. 


1569. The Top Connection.—The angles of which 
the intermediate post is composed connect on the inside of 
plates that are for that purpose riveted on the inside of the 
channels of the upper chord. The live and dead load 
stresses upon the intermediate post are, respectively, 9,700 
and 2,300 pounds. Neglecting the reduction for column 
length, the live and dead load unit stresses allowed upon the 
post are 8,750 and 17,500 pounds per square inch, respect- 
ively. Allowed shearing stresses upon a 3” rivet, at three- 
quarters the unit stresses allowed upon the member = 
8,750 X # X.38068 = 2,010 pounds for live load stress, and 


952 DETAILS OF CONSTRUCTION. 


17,500 x 2 x .3068 = 4,030 pounds for dead load stress. 
Hence, the total number of rivets required by this condi- 
tion for connecting the angles of the intermediate post to 
the plates riveted upon the inside of the channels of the 
9,700 , 2,300 
2.010 ' 4,030 

At 9,000 pounds per square inch, the value of a 8" rivet 
in single shear, as givene by Table 38, Art. 1537, 1s 
2,760 pounds. Hence, the number of rivets required for 
9,700 + 2,300 

2, 760 


=). 4, OT, practically tanl vers 





chord is 


the same purpose by this condition is = 4.3, 


or, practically, 5 rivets. 

The thickness of metal in the angles of the interme- 
diate post is + of an inch. At 15,000 pounds per square 
inch, Table 87; rt. 537, ives the pearing ear 
of a 8” rivet through 1” thickness of metal at - 2,340 
pounds.. Hence, the number “of rivets required bymtmis 
9,700 + 2,300 


2, 340 = D.ds-Olg plactin 


condition for bearing stress is 


cally, 6 rivets. 

At one and one-half times the unit stresses allowed upon 
the post, the bearing value for live load stress of a 2” rivet 
through }” thickness of plate is 8,750 x 3 x § x $= 2,050 
pounds, and for dead load stress, 2,050 x 2 = 4,100 pounds. 
Hence, the number of rivets required by this condition is 
9,700 _ 2,300 
2.050 aE 4,100 

Therefore, it is found that (5.4) 6 rivets, if machine driven, 
will meet all the requirements. 

But the rivets connecting the angles of the intermediate 
post to the plates riveted upon the inside of the channels of 
the chord are necessarily field driven. 

According to the latter portion of item (a@,) of the speci- 
fications, the specified limits of shearing and bearing stress 
must, for field riveting, be reduced one-third part; or, what 
amounts to the same thing, the number of rivets, as required 
by the limits specified for shearing and bearing, must, for 
field rivets, be increased one-half. Consequently, the number 





='§.9, Or, practically 6:t1vets: 


DETAILS OF CONSTRUCTION. 953 


of field rivets required in the present case is 14 x 5.4 = 8.1, 
or, practically, 8 rivets. 


1570. The preceding computations may be a little 
shortened by means of the following formulas, in which d= 
diameter of rivet, = thickness of plate, and Z, D, u, and 
A have the same meanings as in formulas 166 and 168. 

Number of rivets required by shearing stress at 9,000 per 
square inch, 

L+D 


N,, — 9,000 A” C77.) 


Number required for bearing stress, at 15,000 per square 
inch, 
L+D 


zz... = =. 
5s 15 000a2 


(178.) 


Number required for shearing, at # unit stress on member, 


yas) 
gee, i: 


Number required for bearing, at 


3 
. 224 D_ 222+ D) 
ena? 8x Bala 


The values of 9,000 A are given by Table 38, Art. 1537, 
and those of 15,000 @ ¢ by Table 37, same article. 

Instead of computing all the values, we proceed as fol- 
lows: Since z, and z,, have the same numerator, that will 
be greater which has the smaller denominator; but, as 
9,000 A and 15,000 d¢ have the common factor 3,000, we 
only have to compare 3 A andid/?. In the present case, 
34 = 3 X .38068 = .9204, and.56 d#=5x 8X +=28xX4= 
“7+. It is not necessary to continue the latter operation, 
as it is seen at once that the result will be smaller than 3 A. 
Therefore, 7,, 1s greater than z,,and formula 178 should 
be used (15,000 d@ ¢ = 2,340, as given by Table 37). The 
result is 5.1, as found before. 

In a similar manner, to find whether 179 or 180 should 
be used, we compare 3 Au with 6d¢ uw, or, since 3 u is 





il 


(179.) 


unit stress on member, 





(180.) 


954 DETAILS OF CONSTRUCTION. 


common, we compare A and 2d¢. Now, A =.3068, and 
Qeat=2xsx P= B= .31+, whichis greater thang 
Therefore, z, is greater than z,, and formula 179 should 
be used. This gives 

1 2 (19,400 + 2,300) _ 2,170 

*— “3 3008x8150 BC Dna OTe 











— 5.4, 


as found before. 
In all computations where the same rules are used, it is 
convenient to construct a general formula, as this saves 
time and often suggests very short methods for finding the 
required results. The preceding formulas are derived by 
very simple arithmetical reasoning, and it would be a good 
exercise for the student to try to derive them himself. 


1571. The width of the post, perpendicular to lattice 
bars, is 34 -+4-+ 34 = 74 inches. Plates 74” x 7" are used 
for the connection. As the distance from back to back of 
the channels in the upper chord is 74 inches, the clear width 
between these connecting plates is 74 — 2 x 4% = 64 inches. 
The post is given no clearance between these plates, but its 
width, parallel to lattice bars, is made the same as the clear 
distance between the plates, 1.-e., 6 inches. As the upper 
ends of the angles of the post extend but } of an inch above 
the lower edges of the channels of the chord, the post can 
probably be placed in position without clearance, but it 
would usually be better to give a clearance of ;', of an inch 
on each side, making the width of the post, in this case, 
62 inches. 


1572. Spacing for Rivet Lines in Angles.—The 
lattice bars will be 4 of an inch thick, and, in order that two 
bars can connect upon each rivet between the angles, the 
latter must be }-++4=4 inch apart. Batten plates 1” thick 
are used at the ends, requiring also filler plates #” thick 
between the angles, except at the two rivets where the 
lattice bars connect upon the batten plates. 

As was stated in Mechanical Drawing, Art. 56, the posi- 
tion of the rivet line in an angle bar is always fixed by the 


DETAILS OF CONSTRUCTION. 955 


distance from the back or corner of the angle. For this 
distance the values given by the following formula agree 
with most of the adopted standards: 
t 
pe 5 + ¢, CES 1:) 

in which @ is the distance from the back or corner of the 
angle to the center of the rivet hole, d is 
the nominal length of the leg (see Fig. 318), ~-a — ; 
and ¢ is a constant, having the following 
values: 


= 


For values of d of 14" or less, ¢ = A 


6 . 





For values of d of from 2” to 23?”,c=}’. 
For values of d of from 3” to 5’, c= }’. 
For values of @ above 5", hoe FIG. 818. 


These values of c, when substituted in formula 181, will 
give the values of a that agree with what is probably the 
most common practice. But, as in the case of channels, 
the practice is not uniform, though it is more nearly so. 
For instance, it is not uncommon to give ¢ a value of 4 of 
an inch for values of @ of from 14 to 24 inches, inclu- 
sive. 

In the intermediate post, the connected leg of the angle 
is 2 inches wide =d. Hence, by formula 181, the distance 
from the back of the angle to the rivet line is } + 4 =1{ inches. 
This fixes the distance between rivet lines at 6 —2 x 141 = 
48 inches. 


1573. The Bottom Connections.—The rivets con- 
necting the pin plates at the lower end of the post with the 
free legs of the angles are staggered with those connecting 
the angles with the batten plates. As the stress upon the 
post requires the same number of rivets to connect it at the 
bottom as at the top, it is evident that more rivets are used 
to connect the pin plates at the lower end of the post than 
are required by the stresses. 

The pin plates should be thick enough to give the required 


IT. [1,—22 


956 DETAILS OF CONSTRUCTION. 


bearing upon the lower chord pin. Applying rule given in 
Art: 1531, we ‘see that! 3.x 2;90081S* Jess thane o0m 
Therefore, the required thickness is given by formula 166, 
as follows: 


_ 2X 9,700 + 2,300 ; 
oe TS Te WE Ee eo} 5 
LO iC RUE IB FROM eT eae 
This would require each pin plate to be only 3;", but such 
thickness would be too small for strut resistance. 


1574. Forked Ends of Compression Members.— 
Item (¢,) of the specifications (Art. 1511) requires that 
‘Where the ends of compression members are forked to con- 
nect to the pins, the aggregate compressive strength of these 
forked ends must equal the compressive strength of the body 
of the members.” 

The pin plates form the forked ends of the post. In order 
that the angles forming the post may clear the ends of all 
other members connecting upon the pin, the pin plates must 
project beyond the ends of the angles a distance depending 
- upon the dimensions of the other connecting members. The 
aggregate sectional area of the pin plates should not be less 
than that of the angles forming the post. These angles 
weigh 4.4 pounds per foot, giving an aggregate sectional 
area of. 4.4 4 43, = 5.28 square inches. The post: is 

4 inches wide, and pin plates of the same width and 2 of 
an inch thick will give an aggregate sectional area of 74 x 
2X 2= 5.63 square inches. 


1575. The strut resistance of these pin plates will now 
be investigated. The length of the strut formed by a pin 
plate may be taken as the distance between its bearing upon 
the pin and the first rivet connecting it to the angles, if the 
batten plate supports or stays the angles at or very near 
their ends. It will be on the side of safety, in such a case, 
to take the distance between the center of the pin hole and 
the center of the first rivet as the strut length of the pin 
plates. In the present case, the distance is 6 inches. 


DETAILSVORFCONSTRUGTION: 957 


According to formula 140, Art. 1433, the least radius of 
gyration of each pin plate is equal to .289 x 2 =.1084 of an 
inch. Hence, the live load unit stress, as allowed by formula 
125, Art. 1410, is 8,750 —50 x =" = 5,980 pounds. 
The dead load unit stress is 5,980 x 2 = 11,960 pounds. The 
area necessary to resist the stresses upon the post is, there- 
fore, eee + Be aie 

5,980 —§ 11,960 
the sectional area given by the two pin plates is 5.63 square 
inches. It is, therefore, found that the strut resistance of 
these pin plates is ample, when computed upon the same 
basis as the resistance of the post as a whole. 

Considered as struts, the two pin plates will bear 5.63 x 
5,980 = 33,670 pounds of live load stress. The rivets con- 
necting the pin plates to the angles of the post should have 
nearly the same resistance as the pin plates considered as 
struts. At 9,000 pounds per square inch, the value of a 3” 
rivet in single shear is 2,760 pounds. (Table 38, Art. 1537.) 
The metal in the angles forming the post is + of an inch 
thick. At 15,000 pounds per square inch, the bearing value 
of a 3” rivet through 4+ of an inch thickness of metal is 
2,340 pounds. (Table 37.) The latter is the critical condi- 
tion. Hence, in order that the rivets connecting the pin 
plates to the angles shall have the same resistance as the pin 
plates considered as struts, the number of rivets required 
for this purpose is saree = 14.4 rivets. Twelve rivets are 
used for this connection, which is nearly twice the number 
required by the live and dead load stresses in the post, as 
found for the connection of the top of the post. The pin 
plates at the bottom of the intermediate post do not strictly 
comply with ail requirements as indicated in item (¢,) of the 
specifications, but they may be considered practically to 
fulfil the really important requirement of that item; namely, 
that the aggregate compressive strength of the forked end 
shall equal the compressive strength of the body of the 


member. 


= 1.81 squareinches. As found above, 





958 DETAILS OF CONSTRUCTION. 


CONSTRUCTIVE DETAILS OF THE PORTAL 
BRACING. 

1576. Conditions Governing the Arrangement 
of Lattice Bars.—The portal is shown in Mechanical 
Drawing Plate; Titler Hiohway “Bridge: Details Tl Big aan 
The design of the details of this member consists principally 
in determining the proper arrangement and dimensions of 
its connections, and also the arrangement of the lattice bars, 
and their connections with the flange angles. These are for 
the most part questions of judgment rather than of calcula- 
tion. Certain conditions, however, which are susceptible of 
calculation, must be fulfilled. The conditions governing 
the arrangement of the-lattice bars will first be noticed. 

The lattice bars must be connected to and support the flange 
angles at such frequent intervals that the strut resistance of 
the flange in the plane of the lattice bars will be at least as 
great as its resistance in a plane perpendicular to the lat- 
tice bars, as determined in proportioning the material for the 
flanges. In order that this may be the case, the distance /, 
between the rivets connecting the lattice bars to the flanges, 
in inches, must never be greater than given by the formula 


Lies a) (182.) 


in which / is the length of the portal flange (usually taken 
center to center of chords), 7 is the radius of gyration of 
same about an axis parallel to plane of the lattice bars, and 


vy, is the radius of gyration of the same about an axis per- 


pendicular to plane of the lattice bars, all 
in inches. 

The value of 7 is given in formula 113, 
Art. 1408. 

Fic. 319. For two angles with the shorter legs 
connected back to back, but separated by lattice bars (see 
Fig. 319), the value of the radius of gyration about an axis 
parallel to longer flanges of angles, i. e., the value of 7,, is 
given by the formula 





28 
r= 100 V. (1 83.) 


DETAILS OF CONSTRUCTION. God! 


For any ordinary section, the value of 7,, as given by for- 
mula 183, will never be less than one-fourth the value of 7, 
as given by formula 113, and it will seldom have a value so 
relatively small. Hence, the greatest allowed length of /, 
as limited by this condition, may be found by substituting 
47 for 7, in formula 182, as follows: 


We a anus: 
DN erp ae (184.) 
In the present case, the value of 7 is sea Yel, o1nChes. 
and the value of 7, is a x2. 0 = Or ale inches we. vyaiie 


of 7 is 19 feet = 228 inches. Hence, the value of /, must not 


we Soap 
exceed ts * 228 = 88% inches. As determined by formula 
| 228 


184, the value of 7 must not exceec eo 


7 inches, 


which is less than the value just obtained, and very mate- 
rially on the side of safety. 

In compliance with other conditions, however, the pitch 
of the rivets connecting the lattice bars to the flange angles 
can never be made as great as either of the preceding values 
of 7; it is commonly made about 12 inches. Hence, with 
flanges composed of angles connected by lattice bars, this 
condition is never liable to be violated, and may be neglected. 
But there also exists a much more severe condition. 








1577. The pitch of the riv- 
ets along each lattice bar, that 
is, those connecting the bar 
with the lattice bars which cross 
it at right angles, or nearly so, 
and to the flange angles, must 
not exceed a certain multiple of 
the thickness of the bar. This is 
a much more critical condition 
than the preceding. Inorder that 
a lattice bar shall have a reasona- 
ble amount of resistance as a 





960 DETAILS OF CONSTRUCTION. 


strut, its length between connections should not exceed 
about 125 times its least radius of gyration. Formula 
140, Art. 1433, gives the value of the least radius of 
gyration of a rectangular bar = .289 ¢, ¢ being the thickness; 
125 times this = 36 ¢. Hence, the pitch S of the rivets con- 
necting the bars (see Fig. 320) should not exceed the value 
given by the formula 


Sache (185.) 


In the example, the lattice bars are + of an inch in thick. 
ness; consequently, the value of S should not exceed 36 x 
4=9inches. If the lattice bars are placed at an angle of 
45 degrees with the axis of the member, 1. e., at right angles 
to each other, the maximum value of / is given by the 
simple formula 





Veh (BGT seta 807) = Oe Le (186.) 


In the example, ¢ = 4, and the value that 7, must not ex- 
ceed ol & b= 1, ouinches! )Dhis ispthen, the eoverom 
condition. 


1578. In general, if @ and dare the sides, and / the 
hypotenuse of a right-angled triangle, it is well known 
that iat SE 

WV GA 8. 

If a = d, which is always the case when one of the acute 

angles = 45°, we have, 


h=Vei+ai= Va = 2 xX a =1.4142a. (187.) 
Conversely, if 4 is known, the value of a is 
h 
We TE BY or OTL. (188.) 


1579. The Practical Arrangement of the Lattice 
Bars.—In the example the clear width of the roadway is 
18 feet: = 216 inches. At each «side.(end) omthesponraieia 
lattice bars are attached to a somewhat larger vertical bar. 
By trial it is found that by allowing on each side 144 inches 


DETAILS OF CONSTRUCTION. 961 


between the outer line of rivets attaching the lattice bars 
and the inner edge of the upper chord, the space remaining 
between the two outer lines of rivets attaching the lattice 
bars (= 216 — 2.x 144 = 2128”) may be divided into 18 
212.625 ; 

spaces of — ee 11.8125, or 1142 inches each. 

The vertical pitch of the lattice bars is made the same as 
the horizontal pitch, or 114% inches. The legs of the flange 
angles to which the lattice bars attach are 24” long, and by 


formula 181, Art. 1572, the distance from the back of 
21 
the angles to the rivet line is 3 ++34=12 inches. Hence, 








the depth of the portal, from out to out of flange angles, is 
2x 1143+ 2x18 = 268 inches. The space, or pitch, S, 
along the lattice bars, as given by formula 188, is .7071 x 
11.8125 = 8.3526, or 8223 inches. A single space is usually 
expressed to the nearest sixteenth of an inch; but,. in 
case the same space is several times repeated, the error 
thus accumulating may become considerable; hence, in 
thespresent, case, the (pitch of the rivets in the lattice 
bars is expressed to the nearest sixty-fourth of an inch. 
The latticing of the brackets is simply a continuation of 
the latticing of the main or horizontal portion of the 
portal. 


1580. The Portal Connections.—The upper flange 
of the portal is to be riveted to the bent plate shown on top 
of the chord in Mechanical Drawing Plate, Title: Highway 
Bridge: Details I, Fig. 2. It is also to be connected to the 
chord and end post by means of the hip cover-plate, which 
is shown attached to the flange. The details of these con- 
nections are somewhat complicated, but the dimensions of 
the connecting pieces may be determined by accurately 
drawing them in position. The number of rivets required 
to connect the upper flange may readily be determined from 
the stress. The plates used for the connection are 4” thick. 
By reference to Table 37, Art. 1537, it is found that, at 


5” 


15,000 pounds per square inch, the bearing value of a 3 


962 DETAILS OF CONSTRUCTION. 


rivet through a }” plate is 2,340 pounds, while Table 38 of 
the same article gives the value of a 2” rivet in single shear, 
at 9,000 pounds per square inch, to be 2,760 pounds. Hence, . 
the bearing is the critical condition. . The external forces 
acting upon the portal are shown in Fig. 278, Art. 1311. 
By taking moments about the point where the flange of the 
bracket connects to the end post, the stress at the point 
where the upper flange connects to the end post isfound to be 
2,700 K 21 + 4,050 x 5 
5 

ber of rivets required for the connection of the upper flange 
15,390 
2340 
are: to be field driven, eight rivets fare, used = threeusnan 
rivets connect the flange to the hip cover-plate, and five field 
rivets connect it to the bent plate on top of the chord, 
counting as 3-++ 4% X 5= 6.3 rivets. 

The lower horizontal flange of the portal and the lattice 
bars of the bracket attach by means of a 5” x }" plate to an 
angle bar shown riveted on the web of the end-post channel, 
while the flange angles of the bracket are to be riveted 
directly to the web of the channel. It will be noticed that 
the 5” x 4” connecting plate has }” clearance from the web 
of the channel. It would be impossible to determine 
accurately the number of rivets required for this connec- 
tion, but by comparison with the number of rivets required 
for the upper flange, it is seen that a sufficient number is 
used. It is necessary to cut away portions of the connect- 
ing legs of the angles of the bracket flange, in order to con- 
nect between the flanges of the channels of the end post. 
All dimensions of the connecting parts, as well as the 
holes and rivet spacing, must be accurately and plainly 
shown and marked. The dimensions of the connecting 
parts may be determined and the rivet holes located by 
carefully drawing them in place to a sufficiently large 
scale. This need be only a pencil sketch, but it must be 
accurate. It is always well to check the results by calcula- 
tions. 





= 15,390 pounds. Hence, the num- 


of the portal is =, O.TIVELSyal 2iSuiLy Go On LNcoe crits 


DETAILS OP CONSTRUCTION: 963 


CONSTRUCTIVE DETAILS OF THE LATERAL 
STRUTS AND KNEE BRACES. 


1581. The Lateral Strut.—The details of this mem- 
ber are shown in Mechanical Drawing Plate, Title: Highway 
Bridge: Details II, Fig. 2; they are exceedingly simple. The 
strut is to be connected to each chord by means of rivets, 
for which vacant holes-are shown through the horizontal 
legs of the angles. The number of rivets for this purpose 
may be calculated from the initial stress assumed upon the 
strut. The thickness of metal in the angles of the strut is 
2 of an inch, while in the chord the rivets pass through 
both the cover-plate and the cover splice plate, or 4 inch 
thickness of metal. At 15,000 pounds per square inch, the 
bearing value of a 2” rivet through 2 of an inch thickness of 
metal is found to be 3,520 pounds (Table 37, Art. 1537), 
while at 9,000 pounds per square inch the value of a 2” rivet 
in single shear is 2,760 pounds. (Table 58.) The latter is 
the critical condition. In Art. 1425, the resultant stress 
assumed upon the lateral strut was found to be 11,400 pounds. 
Hence, the number of rivets required to connect the end of 


yt Wee Sere) : : 
the lateral strut is 9 760° = 4.1 rivets. As these rivets are 
A,tV0 
field driven, there will be required 14 x 4.1=6.2; 6 are 


used. 

At each end of the strut the two middle holes connect at 
the center of the cover-plate of the chord, while two holes 
connect at each line of rivets connecting the cover-plate to 


93 . 
the channels; hence, these holes are spaced = = 4 inches 


apart. The distance from the two middle holes at one end 
of the strut to the corresponding holes at the opposite end 
is 19 feet, or the same as the distance from center to center 
of chords. The longer or 5” legs of the angles are riveted 
together, back to back. By formula 181, Art. 1572, the 
rivet line is fixed at $+ += 22 inches from the corners of 
the angles. The pitch of the rivets connecting the two 
angles together will not, within any reasonable limits, be so 
great as to weaken the member as a strut; hence, within 


964 DETAILS OF CONSTRUCTION. 


such limits, these rivets may be given any convenient pitch. 
A good rule for such cases is as follows: 


Rule.—/n angles connected closely together, back to back, 
make the pitch of the rivets, based upon the thickness of the 
angles, double that allowed by item (d,) of the spectfications 
(Art US 1): 

Thus, inthe example, the pitch of the rivets connecting 
the vertical Jegs of the angles composing the lateral strut is 
16 X 2 X 2 = 12 inches. 


1582. The Knee Brace.— The form of the section of 
the knee brace, Fig. 3 of plate referred to in the preceding 
article, is similar to that of the lateral strut. The brace is 
usually inclined at an angle of 45 degrees. The horizontal 
and vertical projections of the inclined portion of the brace 
are usually made about 3 feet. In the present case, each is 
made 3’ 02”, or 36.375 inches; hence, by formula 187, the 
length from bend to bend is 1.4142 x 36.375 = 51.4415, or, 
very closely, 4’ 3”. 

The lower end of the brace attaches to the angles of the 
intermediate post. As the post is 6f inches wide, from out 
to out of angles, and the inner rivet holes through the end 
of the brace to connect it with the lateral strut are 1%,” from 
the bend, it follows that ox the lateral strut the distance 
from the middle pair of rivet. holes at the end of the strut 
(at center of chord) to the nearest pair of holes connecting 


. 64 : ; 
the knee brace is oF + 362+ 1% = 412 inches. Deducting 


one space of 4 inches at the end of the strut, we get 412 — 
4q = 364”, or 3' 04”, as marked upon the strut. The posi- 
tions of the holes in the angles of the intermediate post for 
the connection of the knee brace are determined in a similar 
manner. 

The 3” legs of the angles are riveted together, back to 
back. The distance from the backs of the angles to the rivet 
line, as fixed by formula 181, is 3+4=1inches. Ac- 
cording to the rule given above, the pitch of the rivets is 


DETAILS OF CONSTRUCTION. 965 


made double that allowed by item (d,) of the specifications. 
The vacant holes in the knee brace are placed rather nearer 
to the outer edges of the angles than is usual, better to 
accommodate the holes in the angles of the post and strut. 


1583. The Shoe Strut.—This member, which is 
shown in Mechanical Drawing Plate, Title: Highway 
Bridge: Details III, Fig. 4, is a lateral strut, and will next 
be noticed. It can not be completely detailed until the di- 
mensions of the shoe are determined, but as the details for 
this member are so simple as to require very little special 
explanation, they will here be briefly noticed. 

The angles are riveted together with the shorter legs back 
to back, and the plate between them. ‘The spacing of the 
rivets is determined according to the rule given above for 
the lateral strut, which it resembles in form. The distance 
from the corners of the angles to the rivet line, as fixed by 
formula 181, is = + 4 = 12 inches. 

From Art. 1434, it is known that the shoe strut is pro- 
portioned to resist a resultant stress of 7,260 pounds. At 
9,000 pounds per square inch the value of a 2” rivet in single 
shear is 2,760 pounds (Table 38, Art. 1537), while at 15,000 
pounds per square inch the bearing value of a 2” rivet through 
a 1” plate is 2,340 pounds (Table 37). Hence, the latter is found 
to be the critical condition, and the number of rivets required 
for connecting the end of the shoe strut, if machine driven, is 
7,260 
2, 340 
used. 

When the dimensions of the shoe have been determined, 
the position of the lateral pin in the shoe and the length of 
the shoe strut may be found by drawing a plan of the shoe 
and its lateral connections, similar to that shown in Mechan- 
ical Drawing Plate, Title: Highway Bridge: Details III, 
Fig. 17. The lateral strut must be short enough to clear the 
loop of the lateral rod. 





weil, OF, ib neld driven. J+ 5.) = 4.7 rivets; 4 are 


966 DETAILS’ OP CONSTRUCTION: 


CONSTRUCTIVE DETAILS OF THE FLOOR- 
BEAM. 


1584. Positions of Rivet Lines.—In detailing the 
floor-beam, Mechanical Drawing Plate, Title: Highway 
Bridge;, Details, 11; Figo. 4, it;will beawell first) tomieeene 
positions of the rivet lines for the rivets connecting the flange 
angles to the web-plate, and then determine the required 
spacing of the rivets along the same. The depth of the web- 
plate is 24 inches, but (see Art. 1319) the depth of a floor- 
beam, out to out of flange angles, may be made from } to 4 
of an inch deeper thana web plate. Inthe present case the 
depth of the beam, out to out of flange angles, is made 4” 
deeper than the web-plate, or 244 inches. The flange angles 
are’4” 3" angles with the 3 levs conmectedstag tomy er 
As fixed by formula 181, the rivet lines are 3+ 14= 1?inches 
from the backs of the free legs of the angles, making the dis- 
tance betwen the rivet lines of the upper and lower flanges 
244 — 2 x 12 = 21 inches. 


1585. Bending Moments and Increments of 
Flange Stress.—The bending stress in the floor-beam is 
zero at the supports and increases to maximum at the center 
of the beam, while the shear is maximum at the supports 
and diminishes to zero at the center. This is true of any 
simple beam supporting a uniform load, and it is true of a 
simple beam supporting any load or system of loads, with the 
exception that the maximum bending stress and zero shear 
may occur at some point other than the center of the beam. 
The stress, which at the point of support is wholly a shear- 
ing stress, gradually changes towards the center of the beam, 
till at the point of maximum bending moment it becomes 
wholly a bending stress. The change, however, is not uni- 
form, but more rapid near the supports. Under the assump- 
tion that the bending stress is borne entirely by the flanges, 
and the shearing stress is borne wholly by the web-plate, it 
is evident that between any two points the rivets connecting 
the flange angles to the web-plate must be of sufficient 
strength to transfer to the web-plate the difference between 


DETAILS OF CONSTRUCTION. 967 


the bending stresses at those two points. When the load 
rests upon the upper flange, the rivets connecting it to the 
web-plate must also be of sufficient strength to transmit 
the pressure of the load to the web as shear, although 
this is done largely by the stiffeners, when the latter are 
used. 

The bending moment J/, at any point along the loaded 
portion of the beam is given by formula 98, Art. 1318. 
By applying this formula at the center of the beam and at 
certain intervals (say at each foot) along its length towards 
the end, and dividing each result by the effective depth of 
the beam, the several quotients will be the flange stresses 
at the respective points along the half length of the beam. 
The stress increment, or difference between the flange 
stresses at any two consecutive points, must be taken by the 
rivets connecting the angles to the web-plate in that portion 
of the beam included between the two points. 


1586. The Pitch of Rivets in the Flange.—lf the 
stress increment be divided by the critical resisting value of 
one rivet, the quotient will be the number of rivets required 
between the two points. Although this method is quite 
commonly employed, the same result may be more easily 
obtained by the following method: 

Assuming the shear to be resisted entirely by the web- 
plate, and the bending stress to be resisted wholly by the 
flange angles, the pitch fof the rivets connecting the flange 
angles to the web-plate is given by the following formula: 

rh 


in which 7 is the least, or critical, value of one rivet, / is the 
distance between the rivet linesin the two flanges, and Sis the 
vertical shear in the beam at the point under consider- 
ation. 

The rivets connecting the flange angles to the web-plate 
are in double shear. From Table 38, Art. 1537, it is found 
that at 9,000 pounds per square inch, the shearing value of 


968 DETAILS OF CONSTRUCTION. 


a 8-inch rivet in double shear is 5,520 pounds. At 15,000 
pounds per square inch, the bearing value of a g-inch rivet 
through 2 of an inch thickness of plate, as given by Table 37, 
is 3,520 pounds. The bearing is thus found to be the critical 
condition, and 3,520 pounds is the value to be given to 7 in 
the preceding formula. As stated above, the distance % 
between the rivet lines in the upper and lower flanges is 21 
inches. 

S varies in intensity at different points along the beam, 
being, as previously stated, maximum at the supports and 
ZerO;at the Coenen 


As stated in Art. 1227, 


The vertical shear equals the reaction of the left-hand sup- 
port minus all the loads (or all that portion of the uniform 
load) on the beam to the left of the point considered. 


Formula 189 will be applied to the floor-beam at the sup- 
port and at consecutive points one foot apart along the length 
of the beam. From Art. 1316, the total amount of load 
upon the beam is 41,200 pounds. 

But the designer of details must obtain his information, 
from the stress sheet. According to the latter, the maximum 
flange stress is 53,700 pounds. ° The depth of the web-plate 
is 24 inches, and, consequently, the effective depth of the 
beam is 24.5 — 1.5 = 23 inches. Hence, by applying formula 
97, Art. 1318, and dividing by d, the effective depth of 
the, beam. swe @haveswsas.700) ae ae HONE ia ue from 

a 8X 23 j 
which W= 41,170, or, practically, 41,200 pounds. 

As this is a uniform load, the reaction of each support is 
41,200 

2 








= 20,600 pounds, and the load upon each lineal foot 


of the beam is 





4] ; 
a = 2,289, or, practically, 2,290 pounds. 
No load is carried upon the half foot of beam adjacent to 
each support. 
The computations for determining the required pitch of 


the rivets at consecutive points one foot apart along the 


DETAILS OF CONSTRUCTION. 969 


beam are tabulated below. The results in column (ce) will 
be referred to further along: 

















(2) (2) (¢) (¢) (2) 
Required 
Distance of | Amount of Shear at Pitch for Final 
Point from | Load at Left Point, Rivets, Piteh, 
Support. of Point. S=20,600—(2) p= a a’ b,, a' cy, etc. 
Feet. Pounds. Pounds. Inches. Inches. 
O 0,000 20, 600 go00 a.09 
1 1,140 19,460 3.80 Bey 
2 3,430 17,170 4.31 4.20 
o 5, 720 14, 880 4.97 4.81 
4 8,010 12,590 5.87 5.61 
i) 10,300 10,500 Tako 6.72 
6 12,590 8,010 
i 14,880 5, 720 
8 17,170 3,430 
9 19,460 1,140 








As the pitch of the rivets must not exceed 6 inches, the 
computations are completed only to a point 5 feet from the 
support, where the computed pitch becomes 7.18 inches. It 
will be sufficiently accurate to apply each computed pitch to 
that portion of the beam extending 6 inches in each direction 
from the point considered. | 


1587. Effect of Vertical Load; Final Pitch.— 
As the beam is loaded along its upper flange, the rivets in 
this flange must, as previously stated, bear also the pressure 
due to the load upon the beam, exclusive of the weight of the 
beam itself. From Art. 1315, it may be found that the 
estimated load supported by the floor-beam, exclusive of its 


1 1 39,9 
own weight, is 32,400 + 7,540 = 39,940 pounds, or or os 
185 pounds per lineal zzch of the loaded portion. But it 1s 


usually necessary for the designer of details to get all his 





970 DETAILS OF CONSTRUCTION. 


information from the stress sheet. As previously deter- 
mined, the total estimated load upon the loaded portion of 
the beam is 2,290 pounds per lineal foot. From this is to 
be deducted the weight per foot of the beam itself. The 
weight per foot of flanges is 4 x 8.4 = 33.6 pounds, and the 
weight per foot of the web is 24 x @ x 42= 30 pounds, 
making 33.6 + 30 = 63.6 for flanges and web. If 10 per 
cent. be added for weight of details, it will make a total of 
63.6 X 1.10 = 70 pounds (nearly) per foot. Hence, the load 
per foot upon the upper flange of the beam is 2,290 — 70 = 
2,220 pounds, making the load upon each lineal inch of the 
2, 220 
12 
This load produces vertical pressure or stress upon the 
rivets connecting the upper flange angles to the web-plate 
at all points aiong the loaded portion of the beam, while the 
increments of the flange stress act upon the same rivets as 
horizontal stresses. The stresses borne by the rivets are the 
resultants of these vertical and horizontal stresses. The 
pitch, as given in column (d@) of the preceding table, pro- 
vides for the horizontal stresses only, and must be reduced 
so as to provide for the vertical stresses also. The pitch 
thus reduced may be called the final pitch, and can be 
determined graphically more easily than by calculation. 


1588. _ If zis the vertical load upon each lineal zuch of 


flange equal to 





= 185 pounds, as found before. 











FIG. 321. 


the loaded flange, and f and 7 represent the same values as 


DETAILS OF CONSTRUCTION. 971 


in formula 189, the graphical construction giving the final 
pitch is as follows: 


Construct a right-angled trian- 





ze 
SS ! . 3 ok ; 
6 x 33 21" ——» $22 sie, ee ab, fig. 321, sate base 
a ror S35 aais by any convente , 
Seonor: SRO se 3 Vy ANY ventent scale made 







© 


' 
—* 


fea 


equal to the quantity ~ , considered 


! 
i 
1 
1 


as inches, and whose Lae abis 
3 by the same scale made equal to the 
pitch p in inches, as obtained by 
| formula189. froma’ layoffa'l’ 
on the hypotenuse equal toab=f, 
and bya vertical line, as b' b., pro- 





| ant 


EX6 


4 
erat ‘8459 ‘'e* 


an 
10 


v7] 





Sek ject a' b' upon the base of the trt- 
“ ane angle. The projected line a' b, thus 
—F ? F obtained will be the pitch neces- 
ain sary to resist the resultant of the 
13 g .; horizontal and vertical stresses. 
E : 








All the necessary eonstructions 
for the various points along a beam 
are readily combined in one figure. 
In Fig. 321 are combined the con- 
structions for determining the final 
pitch in the six items (except the 
first) of the calculations tabulated 
above. The triangles have a com- 


| 
1,91 
{ 
“Lg 
er ee 


aa 





i 

i 

1 

| 
oie aioe 

' 
—< — 


o39*0F—— 
sae 
oe eee 


CP iae r 
mon base, which is equal to a 


3,520 
185 

of the several triangles are equal 
to the pitch required by the re- 


—19inches. The altitudes 





—,059 
—+— 
eI 





| 

’ | 
aa 

’ 

{ 
i — 

i] 
—PiG——a 


| S spective stress increments, as given 

| | | in column (d) of the table in Art. 

Wanita hean tha 1586 (except first item). The 
FIG, 822. final pitches, i. e., the results a’ 0, 


a’ c,,etc., are given in column (2) of the same table. As 
there is no vertical load upon the upper flange at the 
T. II,—23 


972 DETAILS OF CONSTRUCTION. 


support, the pitch at that point is given the same in column 
(¢) as in column (d@). For that point, the pitch as given 
in column (2) is the final pitch. 

The rivet spacing along the flange, giving the pitch of 
rivets as required and used, is clearly shown in Fig. 322. 
Near the end of the beam the pitch is made somewhat less 
than the required pitch, on account of the connections for 
the lateral rods. The rivet spacing in the lower flange 
should usually be made the same as in the upper flange. 


1589. Stiffeners.—In each stiffener the pitch of the 
rivets should not exceed that required in the adjacent por- 
tion of the flange. For practical considerations, however, 
it is desirable that when possible the pitch of rivets should 
be uniform in all stiffeners on the same beam. Single 
stiffeners are sometimes used on the floor-beams of highway 
bridges, being placed alternately on either side of the beam. 
The practice, however, is not to be commended. 

If the beam is supported upon its 
bottom flange, as in the present case, it 
should have two pairs of stiffeners at 
the end, in order to transmit properly 
the shear upon the bearing. In case of 
heavy beams and plate girders, that por- 
tion of the web above the bearings should 
be also reinforced by additional plates. 
Were this necessary in the example it 
could readily be accomplished by using a 
vd” < 2" X 184” plate on each side of the 
web-plate, extending as a filler plate 
under the two end stiffeners. As stated 
in Art. 1448, stiffeners are not neces- 
sary in this case, but are used simply as an 
illustration. They should always be used 
at the ends of floor-beams. 

stiffeners are sometimes used without 
| fillers, in which case the stiffener angles 
Fic. 323, must be offset or crimped to fit over the 





DETAILS OF CONSTRUCTION. 973 


legs of the flange angles, as in the end view of the beam 
shown in Fig. 323. It is not economy to do this, however, 
except in heavy beams. In light beams the cost of offset- 
ting the angles will usually be greater than the cost of the 
material for fillers. 


1590. Positions of Beam Hangers.—The positions 
of the holes for the beam hangers through the horizontal 
legs of the flange angles are fixed longitudinally of the beam 
by the length of the beam from center to center of chords. 
Their distance apart across the flange, as well.as the diam- 
eters of the holes, are determined by the dimensions of the 
hanger [ Mechanical Drawing Plate, Title: Highway Bridge: 
Details IV, Fig. 7]. The end of the beam must project a 
sufficient distance beyond the hanger holes to afford a bear- 
ing for the end of the intermediate post, this being necessary 
to hold the beam securely in position. 


1591. The Connections for Lateral Rods.—The 
details of the plate and angle lugs for lateral connections are 
largely matters of arrangement, but sufficient bearing for 
the lateral pins must be provided. As the four floor-beams 
are made alike, the bearings for the lateral pins must be 
sufficient to resist the greatest stress upon any lateral rod 
attaching to the beam. The rod in the end panel of the 
lower lateral system is 1{ inches in diameter, and bears a 
stress of 14,900 pounds. In order to admit this size of rod 
the clear distance between the angle lug and horizontal leg 
of the angle of the top flange should not be less than 
lt inches. As the rivets attaching the plate for the lateral 
connection to the flange angles must be countersunk on the 
under side, requiring ample clearance, the top of the angle 
lug is placed at the center of the flange rivets, giving a 
clearance between the bearings for the lateral pin of 
13—%=18inches. The holes for the lateral pins are so 
near to the edges of the flange angles that the resistance of 
the latter should not be counted. Hence, neglecting the 
bearing of the flange angle, the distance between the centers 
of the bearings for the lateral pins is 13+ $= 24 inches. 


974. DETAILS OF CONSTRUCTION: 


By applying formula 106, Art. 1371, the bending moment 
14,900 x 24 
4 
From Table 40, Art. 1546, it is found that, with a fiber 
stress of 18,000 pounds per square inch, a pin 1? inches in 
diameter will give the required resisting moment. From 
the same table it is found that, at 15,000 pounds per square 
inch, the bearing value of a 1?” pin through 1 inch thick- 
ness of metal is 26,300 pounds. Hence, the total thickness 
14,900 _ 
26,300 
inch. Two bearings, each 75 of an inch thick, giving a 
total bearing of 2 xX = #% (.63) of an inch, will give the 
required bearing surface. As, however, the vertical leg 
of the angle lug is subjected to a certain amount of bend- 
ing stress, the metal in the angle is given a thickness of 2 of 
an inch; the plate on top of the flange is given the same 

thickness. 

At 9,000 pounds per square inch, the shearing value of a 
5” rivet is 2,760 pounds (Table 38, Art. 1537), which is less 
than its bearing value througha 2 inch plate at 15,000 pounds 
per square inch ( = 3,520 Ib., Table 37). Consequently, as the 
pin plate is subjected to one-half the stress upon the lateral 
rod, the number of rivets required to connect the plate to 
14,900 
2, 760 
Four rivets are used. 





upon the pin is found to be = 7,920 inch-pounds. 


of bearing required for the lateral pin is OO Olean 





the flange is 4X 





— in, (5. OTs. DLACLICALLY) = oe TI VeLas 


1592. Asit is not permissible to use rivets in tension, 
the angle lugs are attached by means of bolts. The sec- 
tional area of the 13” lateral rod is .99 of a square inch, and 
it will be practically correct to make the aggregate sectional 
area of the two bolts somewhat more than one-half of this 
amount. After deducting the section cut away by the 
threads, the sectional area given by two #" bolts is about .6 
of a square inch. | 

The lateral connections on the floor-beam should be placed 
as near to the beam hangers as other necessary conditions 


DETAILS OF CONSTRUCTION. 975 


will permit. After the dimensions and positions of the 
lower chord connections are determined, the position of 
the lateral connections on the floor-beam may be fixed by 
drawing plans of the lower chord joints similar to those shown 
in Figs. 15 and 16 of the plate just referred to. 


TENSION MEMBERS. 


EYE-BAR HEADS. 


1593. General Requirements and Manufacture. 
—In pin-connected trusses the main tension members are 
usually composed of eye-bars. The relative dimensions of 
eye-bar heads will now be considered. Item (/7,) of the 
specifications requires that ‘‘ The heads of eye-bars shall be 
so proportioned and made that the bars will preferably 
break in the body of the original bar, rather than at any part 
of the head or neck.”’ 

The heads of wrought-iron eye-bars are commonly formed 
by piling the proper amount of scrap iron, carefully selected 
and suitably arranged, upon the end of the bar, and then, 
after heating to the required temperature, forging the head 
into the desired shape ina die under a steam hammer or 
hydraulic pressure. Other similar processes are occasionally 
employed. If the welding is perfect, the head becomes 
thoroughly identified with the bar; but this is seldom the 
case. Nevertheless, wrought-iron eye-bars have been very 
commonly produced by the process indicated above which, 
when tested to destruction, would break in the body of the 
bar, rather than in the head or neck. 

Eye-bars are now quite generally made of medium steel, a 
material which has been found excellent for this purpose. 
Steel eye-bars are usually formed by first upsetting the bar 
sufficiently to form the head, then forging the latter into 
the required form in a die under steam or hydraulic pres- 
sure. The bars thus obtained are very satisfactory. Steel 
eye-bars have, however, been successfully made by piling 
carefully selected scrap and forging, in much the same 


976 DETAILS OF CONSTRUCTION. 


manner as for wrought-iron eye-bars; but great care is 
required in the arrangement of the scrap and in the forging, 
and a suitable quality of steel is required for both the bar 
and the scrap. Whatever the process of manufacture, the 
bars must be subsequently reheated and annealed before 
boring the pin holes; this should never be omitted. 


1594. Dimensions of Wrought-Iron Eye-Bar 
Heads.—The relative dimensions of eye-bar heads to fulfil 
the conditions of item (7,), quoted above, are determined by 
experiment. A form of head which has been very exten- 
sively used for wrought-iron eye-bars is shown in Fig, 324. 


i) 


‘ 
Ce a ee 






(a eee Q 


ee 
2 


FIG, 324. 

If the thickness of the head is the same as that of the 
original bar, the dimensions of the head may be expressed 
in terms of w, the width of the original bar. The dimen- 
sions a and a’ (see Fig. 324) are each given by the formula 


a=a= hw. (190.) 
CA=CA' = radius of pinchole=9) 4 - D ande a e 
straight lines parallel to the center line of the bar. DB D' 
is a semicircle of radius d D=7--a, with the position of 


the center A so taken on the center line of the bar that the 
dimension @ will have the value given by the formula 


b= $w. (191.) 


DETAILS OF CONSTRUCTION. vets 


This makes CA =r—(A D—d)=r—(r+iw—tw) 
=, w. &:-F and &’ Ff’ are circular arcs having their 
Sentenovatiwivc and -Tadite ee ane deat edusie tO: As J). 
a i= AC. The arcs &.G andl :G ‘should have equal 
radi O F and O’ F', which should be of sufficient length to 
gradually connect the head with the main body of the bar; 
the radius O /of the neck is often made approximately 
equal to one and one-half times the radius A’ /. 

If the heads are made thicker than the body of the bar, the 
letters a, a’, b, and w inthe two preceding formulas must be 
considered to represent sectional areas instead of dimensions, 
the sectional areas to be taken on the respective lines as 
shown in Fig. 324. 


1595. At the present time, however, eye-bar heads are 
generally made circular, as shown in Fig. 325. The center 
ECOL OU Ole IS AL | ect penes 
the center of the i 
head. The dimen- 
sions for this form of 
head being simpler, 
the dies are less ex- 
pensive than for the \ | 
form of head shown \ D 

| 
\ | 






ins Pig. 324. * Ac- \ 
cording to the most \ 
approved practice, \Y 
the net sectional area FIG. 325. 
A through the pin hole (i. e., area d =areas a+a= 
t(D—d), ¢ being the thickness) should not be materially 
less than given by the following formulas, in which B 
represents the sectional area of the body of the bar: 

When the diameter d of the pin hole does not exceed } of the 
wath w of the bar: 


Fi iemoied PLIEY OF (192.) 
When the diameter d of the pin hole materially exceeds the 
width w of the bar: 
ives ees, (193.) 


978 DETAILS OP- CONSTRUCTION: 


If the thickness of the head is the same as the thickness 
of the bar, a+ a' = D —d may be substituted for A, and w 
for 4. For wrought-iron eye-bars with circular heads, as 
used in highway bridges, the net sectional area A across the 
head is often made equal to one and one-half times the 
sectional area of the bar. This practice has, in most cases, 
been found to give satisfactory results. 


1596. Dimensions of Steel Eye-Bar Heads.—Steel 
eye-bar heads, when properly made and annealed, possess 
somewhat greater relative efficiency than those of wrought 
iron, and, consequently, do not require so large a percentage 
of additional material. The heads are generally made cir- 
cular in form, as in Fig. 325, and the thickness of the head 
is always made the same as that of the original bar. (See 
Art. 1512, VII.) If, for steel eye-bars, the et dtmension 
across the head be represented by A, =a-+ a= D—d, 
then this net dimension, as compared with the width w of 
the bar, is given by the following formulas: 

When the diameter dof the pin hole does not exceed % of the 
wath w of the bar: 


A=1.33w. (194.) 


When the diameter ad of the pin hole exceeds the width w of 


the bar: 
A= 14, (195.) 


1597. The diameters Y of eye-bar heads are usually 
expressed nominally in multiples of a half inch; but, as 
actually manufactured, heads whose diameters are multiples 
of an inch are quite commonly made ¢ of an inch less than 
their nominal diameters, in order to admit of being packed 
inside of channels of the same nominal size. 


1598. On account of the practical conditions of manu- 
facture and of the liability of thin eye-bar heads to buckle 
behind the pin hole when under strain, the thickness of the 
head should not be less than given by the following formula: 


 D+w+s 
tremens cat ¢ (196.) 


DETAILS OF CONSTRUCTION. 979 


For highway bridges the minimum limit of thickness 
allowed for eye-bar heads should never be less than 2 of an 
inch. For railroad bridges the minimum limit is 2 of an 
inch, and this limit might properly be applied to all bridges. 


CONSTRUCTIVE DETAILS OF THE LOWER 
CHORD MEMBERS. 


1599. The End Panella b; Bearing on Shoe Pin. 
—The details of the member in the end panel of the lower 
chord are shown in Mechanical Drawing Plate, Title: High- 
way Bridge: Details III, Fig. 1. The end a of this member 
connects upon the shoe pin by means of pin plates riveted 
to the angles composing the member. These pin plates 
must be thick enough to afford sufficient bearing upon the 
pin, and, as they practically fulfil the office of eye-bar heads, 
they must also provide sufficient metal, at the section 
through the pin hole and beyond the pin, to comply with 
the conditions of formulas 190 and 191. 

According to item (0,) of the specifications, as this mem- 
ber is not composed of forged eye-bars, its bearing stress 
upon the pin must not exceed 15,000 pounds per square inch, 
or one and one-half times the unit stress allowed upon 
it. As one and one-half times the allowed unit stresses 
would be 14 x 10,000 = 15,000 pounds, and 14 x 20,000 = 
30,000 pounds per square inch for live and dead load stresses, 
respectively, it is readily seen that an allowed bearing stress 
of 15,000 pounds per square inch for all stresses is the more 
severe requirement. The stress sheet shows the live and 
dead load stresses for this member to be 32,400 pounds and 
13,900 pounds, respectively. At 15,000 pounds per square 
inch, Table 40, Art. 1546, gives 41,300 pounds as the bear- 
ing value of a 24-inch pin through 1 inch thickness of plate. 
Hence, the total thickness of bearing for the pin plates 
46, 300 
41,300 
or about 1} inches. Two pin plates, each $ of an inch 
thick, would give ample bearing surface upon the pin. But 


required by the stresses upon the member is Salolale 


980  -DETAILS OF CONSTRUCTION. 


at the shoe joint, other considerations will require a greater 
thickness for the pin plates upon the chord. 


1600. Section of Pin Plate Across the Pin Hole. 
_—From the stress sheet it is found that the net sectional 
area given by the four angles composing this member is 
4.02 square inches. By applying formula 190, at the sec- 
tion on the lines a and a’ (Fig. 324) through the pin hole, 
and using areas instead of dzmenszons for the values of w 
and a, the net sectional area required at the pin hole is found 
to be 2 X 4 < 4.02 = 5.36 Square inches: Hence, as therpin 
plate is made 64 inches wide, the total thickness of metal 
required for the pin plates by this condition is NTH we mE 
1.43 inches, which is practically ¢ of an inch for each plate. 
But this will probably be found not to be the critical 


condition. 


1601. Critical Section of Pin Plate.—As the space 
between the shoe pin and the cover-plate of the end post is 
limited, it will be necessary to either cut away the cover- 
plate sufficiently to allow the pin plates to project through 
it, or to plane off the corner of each pin plate sufficiently to 
clear the cover-plate. As the former would have a rather 
unworkmanlike appearance, the latter expedient will be em- 
ployed. It will be necessary to cut away a large piece of 
the metal of the pin plate; consequently, the amount of 
metal remaining between the pin 
and the edge of the plate thus 
formed, 1.-¢.4 onpthé line*asar 1 
326, will probably be found to 
be the critical condition in com- 
plying with the requirements, 

aoc and no advantage will be ob- 
tained by making the pin plate wider than the member itself, 
or 3-+4-+3 = 6} inches. 

From Mechanical Drawing Plate, Title: Highway Bridge: 
Details I, Fig. 1, it is known that the distance between the 
center of the pin and the lower side of the cover-plate of 





DETAILS OF CONSTRUCTION. 981 


the end post is 3 inches. Consequently, by allowing |, 
of an inch as the smallest permissible clearance, the net 
width ¢ (see Fig. 326) of that portion of the pin plate 
between the edge of the pin hole and the lower side 
of the cover-plate of the end post can not be more than 
d—% X 23 —7,=— 1%, =1.56 inches. As given by formula 
190, the sectional area required in the vertical section above 
or below the pin hole, i. e., the section on the line a or a’, 
Fig. 326, is 2 x 4.02 = 2.68 square inches, while the sec- 
tional area required on the horizontal section behind the 
pin, 1. e:, on the line 6, is | X 4.02 = 3.52 square inches. 


(Formula 191.) 


1602. In the case of a pin plate having the corner cut 
away, as shown in Fig. 326, in order that the section on the 
line c, making an angle of 45 degrees with the center line of 
the member, shall give practically the same resistance as 
the sections on the lines a and 4, as derived by formulas 190 
and 191, respectively, the sectional area on the line ¢ must 
have the value given by the formula 


C= £6 w, (197.) 


in which w represents the sectional area of the member. In 
the example, therefore, the sectional area required on the 
linec is 38 X 4.02 = 3.14 square inches. 

Hence, the total thickness of the pin plates required by 
this condition is me = 2.01 inches. This is, therefore, the 
governing condition. Two pin plates each 1 inch in thick- 
ness might have been used; instead, however, four pin 
plates each $ inch thick (two double plates) are used. 

As each pin plate is of uniform thickness, the dimensions 
6 andc will be proportional to the area of the sections on 
those lines. The dimensions c and both areas being known, 
we have the proportion 3.14: 3.52 :: 1.56: 4, from which 
ee 3.52 X 1.56 

3.14 
from the center of the pin to the end of the pin plate is 
1.75 + 1.388 = 3.13 inches, or say 34 inches. 


= 175 inches. Hence, the required distance 


982 DETAILS OF CONSTRUCTION. 


1603. Rivets for Connecting Pin Plates.—The 
number of rivets required to connect the pin plate to the 
angles composing the main portion of the member is deter- 
mined by the most severe condition of the requirements for 
the shearing and bearing. The unit stresses allowed upon 
the member are 10,000 and 20,000 pounds for live and dead 
load stresses, respectively. 

As all the determinant conditions (the values of A, d, 
and ¢) are the same as in Art. 1570, formulas 178 and 
179 should be used, and the results compared. As d= 2’, 
and ¢7=4"sTable 37; Art. D537, vives 15000775. sae 
Formula 178 gives 

eg a 32,400 + 13,900 

18 2,340 
2(2 X 32,400 + 13,900) a 
3X .38068 K-10;000 ny 


maa fl 8 rep 





Formula 179 gives 2, = 


The required, number of rivets 1s;.theretore, L0so tide 
is, 20. 

Twenty rivets are used to connect the angles composing 
the member to the pin plates at each end. Sixteen rivets 
(four in each angle) connect the free vertical legs of the 
four angles directly to the pin plates, and four rivets (two 
in each pair of angles) connect the horizontal legs of the 
angles to four short pieces of angles attaching to the pin~ 
plates. It will be noticed that each of the four rivets last 
mentioned has a double bearing value and is also in doubie 
shear, which gives practically a total value of 24 rivets in 
the connection of the pin plates, thus making ample allow- 
ance for countersunk rivets. The details of this connection, 
though fulfilling all requirements, could be somewhat 
improved. 


1604. Pin Plates at Joint b.—For connecting the 
pin plates at the opposite end 0 of the member, the number 
of rivets required is the same. It was found above that two 
pin plates each 2 of an inch thick, or a total thickness of 
14 inches, will give sufficient bearing for this member upon 


a 2¢-inch pin. With a total thickness of 14 inches, the 


DETAILS OF CONSTRUCTION. 983 


required width of the pin plates, as given by applying 
2X xX 4.02 
formula 190, Art. 1594, is get 5 = 7.04 
inches. Two pin plates 7” x 8” will be used. As determined 
by formula 191, the pin plates must project beyond the 
9 

edge of the pin a distance of Oe = 212 inches (very 
closely), or a distance of 212-+ 12 = 4,3, inches beyond the 
center of the pin. It will be well to make this dimension 
practically 44 inches; for convenience in shortening the 
distance between pin centers », of an inch, in compliance 
with the rule given in Art. 1519, this dimension is in- 
creased to 4,°, inches at one end. 


1605. Metal Behind Pin; Another Condition. — 
Pin plates for tension members should not only comply with 
the conditions required by formulas 190 and 191 for eye- 
bar heads, but, besides, the dimension 0, Fig. 326, should 
never be less than given by the following formulas: 

For wrought tron: 


9dt 
b= oT (198.) 
For medium steel: 
at 
og alban re 
b= Tr (199.) 


In both of these formulas d@ is the diameter of the pin 
hole, 7 is the thickness of pin plate required by the bearing 
stress, and 7 is the actual thickness of the pin plate. 

It was found above that the total thickness ¢ for the pin 
plates at each end of this member, as required by the bear- 
ing stress, is 1.12 inches. At the end a of the member, the 
total thickness 7 is 2 inches. Hence, at this end of the 
member the dimension @, or clear distance from the edge of 
the pin hole to the end of the member, must not be less 
than cos aes PAG ss 1.73 inches; or, to express it other- 
wise, the distance from the center of the pin hole to the end 





984 DETAILS OF CONSTRUCTION. 


of the pin plate, as required by this condition, must not be less 
than 1.73 + sls == 3.11 inches. At.the end/Oof the memper 


Ky 6 

the dimension @ should not be less than Mees eS Ree iy if 
inches, making the distance from the center of the pin hole 
to the end of the pin plate, as required by this condition, 
equal to 2.77 + 1.88 =4.15inches. As the distance adopted 
is greater than this, it is found that the condition required 
by formula 198 has been complhed with. 

It will not be necessary to take special notice of the 
arrangement of the lattice bars for this member; it involves 
no unusual or difficult conditions, and will be readily under- 


stood without explanation. 


1606. The Second Panel b c.—The dimensions of 
the pin plates for the member in the second panel 6c of the 
lower chord, Mechanical Drawing Plate, Title: Highway 
Bridge: Details III, Fig. 2, are determined in substantially 
the same manner as explained above for the lower chord 
member a 4; it will be unnecessary to explain the process in 
detail. It will be noticed that the connections of the pin 
plates on this member are more simple than upon the mem- 
ber:a 6, Fig. 1 of the same” plate.) simplicity ot detauerd 
always desirable and should be obtained whenever possible. 
The manner of connecting the pin plates shown in Fig. 
2 (same plate) is far preferable to that shown in Fig. 1. In 
order that the relative widths of the members would be such 
as to connect properly upon the pins, the arrangements of 
the pin plates as shown for the joint a of the member a 0 
became necessary. 

It will be noticed that in the preceding computations the 
dimensions of the pin plates have been proportioned accord- 
ing to the requirements for elongated eye-bar heads. This 
method, although not very generally employed, is given 
here as a safe and reliable practice for the pin plates of 
tension truss members. 


1607. Stiffened Eye-Bars; Panel c c’.—The mem- 
ber in the middle panel of the lower chord is shown in Fig, 3 





DETAILS OF CONSTRUCTION. 985 


of the plate just referred to. It is composed of eye-bars of 
the usual form, except that, in order to illustrate another 
form of stiffened chord, the bars are shown connected by 
bent lattice bars. The heads are of the form shown in Fig. 
325, and, as the diameter of the pin does not exceed three- 
quarters of the width of the bar, the diameters of the heads 
are determined by formula 192. By reference to items 
(o,) and (4) of the specifications, it is found that for forged 
eye-bars no definite limit is placed upon the intensity of 
bearing stress, other conditions being usually such that the 
permissible intensity of bearing stress will not be likely to 
be exceeded. In the present case, however, the thickness 
of the eye-bar heads has been increased to $ of an inch, in 
order that the bearing stress shall not exceed 15,000 pounds 
per square inch. According to the stress sheet the net sec- 
tional area of the member is 6.40 square inches. Hence, by 
formula 192, the net sectional area of the head across the 
pin hole, 1. e., on the lines a and a’, Fig. 325, must be for 
1.6 X 6.40 
5) 


a thickness of { of an inch, the diameter / required for each 


) 


each of the two bars = 5.12 squareinches. With 


ae ibe fie 
head is i A + 2.75 = 8.60inches. Heads nominally 9 inches 


in diameter, but having an actual diameter of 8£ inches, are 
used. 

When the eye-bars are not connected by lattice bars, it is 
necessary to designate only the size of the bar, the diameter 
and thickness of each head, the size of each pin, the distance 
from center to center of pin holes, and the number of bars 
required. In many bridge offices the practice is to simply 
make a list of the eye-bars required for each structure, giv- 
ing the above items; in such cases the eye-bars are not 
shown on drawings, except when required to be latticed. 

In some bridge works it is the practice to state the diam- 
eter of the pzzs to be used, as is shown in Mechanical Draw- 
ing Plates, Titles: Highway Bridge: Details I to IV, while 
in other shops it is the practice to state the exact diameters 
required for the pzx holes. 


986 DETAILS OF CONSTRUCTION. 


It is never necessary to give the radius for the necks of 
eye-bars. As they are always tension members, the distance 
from center to center of pin holes must be shortened 34 of 
an inch, in compliance with the rule given in Art. 1519. 

The’ latticinge “of chord. bars™ is mérely a “matters: 
arrangement, needing no special explanation. 


CONSTRUCTIVE DETAILS OF THE TENSION 
WEB MEMBERS OF THE TRUSS. 


1608. The Main Tie Bars B c.—The dimensions of 
the main tie bar are shown in Mechanical Drawing Plate, 
Title: Highway Bridge: 2Details IV ig 1 See ee ome 
joint, the distance between the center of the pin and the 
cover-plate of the chord, or of the end post, is 3 inches. 
Hence, it is evident that the radius of the eye-bar head 
connecting upon this pin must be slightly less than this. 
The nominal diameter of the head will be 6 inches; the 
actual diameter, 5£ inches. The diameter of the pin hole 
will be somewhat in excess of the width of the bar, but not 
greatly so; consequently, the net sectional area A across 
the head may be taken at a mean between the values given by 


formulas 192 and 193, that is,as equal to a-tis 


The sectional area of one' bar is 2X 142=1.63 square 
inches, and, as the diameter of the head is fixed at 5f£ 
(= 5.875) inches, the thickness of the head must be 
eae ae = «885, or, practically, ~ of an inch. Heads 
5g’ x ¥ will be used. As in the present case it is essential 
that the diameter of the head should under no condition 
exceed 54 inches, the exact diameter of the head is marked, 
instead of its nominal diameter. As the pins at each end 
of the bar are of the same size, both heads will be made 
alike. The length of the tie bar, from center to center of 
pin holes, is 25’ 5". (Art. 1519.) 


1609. The Hip Vertical B b.—A hip vertical rod is 
shown in Fig. 3 of the plate just mentioned; it is 1 inch 


DETAILS OF CONSTRUCTION, 987 


square. Each hip vertical member consists of two rods like 
this. Hip vertical members sometimes consist of ordinary 
eye-bars, however. In the present case the loop, by which 
each end of the rod connects upon the pin, is formed by 
bending the end of the rod into the desired form and weld- 
ing it back upon the bar, making the rod as nearly of the 
desired length as possible. The length of such bars is 
always given between the inner edges of the extremities of 
the two loops, as shown; it is commonly called the length 
back to back, and is designated on drawings by the letters 


Bto B or 6 to 6. 


Rule.—T7he length back to back of a tension rod having 
loop ends ts the length from center to center of pins plus one: 
half the diameter of cach pin, minus 5 of an inch tf the rod 
7s not adjustable. 


Thus, in the present case, the length J fo 6 is equal to 

, Qe" = Qe" , 93/ 

18’ 0" + a ay ay gg = 18 223". The exact length d/o 6 
is finally obtained in reaming the inner sides of the loops to 
fit the pins. 

Rule.—7he inside length of a bent loop ts always made 
equal to 24 diameters of the pin upon which it connects ,; or, 
in other words, the distance from the center of the pin to the 
inner angle of the weld 1s made equal to 2 diameters of the 
pin. 

In the present case, the length of each loop is 24 x 2% = 
6£ inches. 


1610. The Counter Tie -C c’.—Counter ties usually 
consist of square or round bars, though frequently of flat 
bars. The counter shown in Fig. 2 (title as above, IV) isa 
square bar and connects upon the pins by means of bent 
loops in substantially the same manner as the hip vertical. 
The form and relative dimensions of the loop are also the 
same as described for the hip vertical. The two ends of the 
rod connect upon different sizes of pins, and the dimensions 
of each loop depend upon the size of the pin upon which it 
connects; the loop upon the lower end c’ of the rod, connect- 


T. I1.—2?4 


988 DETAILS OF CONSTRUCTION. 


ing upon the 2%” pin, is flattened to ? of an inch in thickness 
in order to pack upon the pin within the required space. 

Counters are made adjustable, usually by means of turn- 
buckles, as shown. Sometimes, however, only one of the 
diagonals in the center panel of a truss is made adjustable. 
This counter tie will be further noticed in the following 
articles. 


UPSET SCREW ENDS. 


1611. The end of rods upon which threads are formed 
are enlarged by upsetting, so that after the threads are cut 
the remaining portion of the end will be as strong as the 
unaltered portion of the rod. As the process of upsetting 
somewhat reduces the strength of the metal, bars in which 
the diameter at the root of the thread is the same as that of 
the bar itself, invariably break in the screw end, when 
tested to destruction, without developing the full strength 
of the bar. It, therefore, becomes necessary to make up 
for this loss of strength by upsetting the ends sufficiently 
so that the sectional area at the root of the thread will be 
somewhat in excess of the sectional area of the bar. 

According to item (#,) of the specifications (Art. 1511), 
‘fall rods and hangers with screw ends shall be upset at the 
ends, so that the diameter at the bottom of the threads shall 
be ;/; inch larger than any part of the body of the bar.” 

According to Thacher’s specifications, ‘‘the area at root 
of thread in the upset ends of rods shall be greater than the 
area of the rod at least 17 per cent.” 

According to Lewis’s specifications, ‘‘the area at base of 
thread and at all parts of upset ends will be 15 per cent. in 
CxcessOl tic areatol tnesvainn 

The common practice, which varies slightly in different 
shops, gives an excess of effective sectional area of the screw 
end over the area of the bar of from about 17 to 50 per cent., 
the diameter of the upset end always being a multiple of 
2 of an inch. 

The following table, which gives the standard proportions 
for upset screw ends as used by the Keystone Bridge Com- 


DE TATE St ORSGO Moi D.C id ON: 


989 


pany, is fairly representative of the best practice for upset 
ends: 


TABLE 41. 


UPSET SCREW ENDS FOR ROUND AND SQUARE BARS. 








Diam. of Kound or Side 
of Square Original Bar. 





I 

178 
174 
138 
1 
14 
134 


1% 


ae 

236 
234 
236 
24 





























Round Bars. Square Bars. 
oJ os eis eh, oJ s ao ts, 
o2 [Eg | Se faa] 28 [53] 38 |e 3 
85 |$4e) 58 |Aun) $5 |Se8) b5 [Fae 
rte eevee dere eis SS nS Ste ary Cfo pS O. © 
aa BSc! 6g lad 0 fia Le Sun) tad 7 tS 
Se a ete ae Mey ae OR ES A ee eg 
Bees eee PAIRS | 4 ble og 
P v7 a |A oe p D eG |A P 
Inches. | Inches. Per cent.|| Inches. | Inches. Percent. 
34, txt lets 54 34 .62; | a0 21 
a ey a) 37 I .84 | 8 41 
I .84 8 25 1% .94 7 23 
1% | 1.07 7 48 13g | 1.16 6 38 
1348 | 1.16] 6 as 5a} 1.28.4 6 29 
Etech Lees |, 20 30 14% | 1.39 | 5% 20 
1544 | 1.39 | 5% 23 Eves etO2it ck a1 
14> \eheao-) 5 18 2 I.91 4% 22 
2 1.71 | 4% 30 2% | 1.84| 4% 18 
24%) 1.84 4% 28 23% | 2.09 4% 30 
24 11.96| 4% 26 2% | 2.18 | 4 21 
23g | 2.09 | 4% 24 258} 2.30 | 4 18 
2% | 2.18 | 4 18 27% | 2.55 |} 4 28 
298 | 2.30 4 7 i. S203 32 20 
Ds Ae pee 28 3% | 2.75 | 3% 18 
4 2.63 | 3% 23 338 | 3.00 | 3% 26 
peea275 Pogiai| 22 Brees STO)| aah | ax 








The diameter of the round bar or side of the square bar 
being known, the corresponding diameter of the upset end 


may be obtained from the table. 
sometimes required on flat bars. 


Upset screw ends are 


In such a case it is neces- 
sary to find first the side of a square bar having the same 


990 DETAILS4OF CONSTRUCTION: 


sectional area as the flat bar, and then to find from the table 
the diameter of the upset end as required for the square bar. 
The length of the upset end may be determined by formula 
200, which is given in connection with the dimensions of 
turnbuckles. 


TURNBUCKLES. 

1612. Having obtained the required diameter of the 
upset screw end, the dimensions of the turnbuckles are next 
to be determined. The threaded ends of the two portions 
of the rod screw into the ends of the turnbuckle, or, in other 
words, the turnbuckle screws upon the ends of the rods by 
means of a right-handed screw at one end and a left-handed 
screw at the other end, so that by turning it inone direction 
both ends are screwed up, while by turning it in the opposite 
direction both ends are unscrewed. As the finished turn- 
buckles commonly used are to be obtained in the market in 
sizes suitable for the different diameters of thread ends, the 
various dimensions of turnbuckles are not commonly given on 
the drawings, it being usually sufficient to designate the 
dimensions of the thread ends and state the sizes of turn- 
buckles to be used. But, in order that the proportions of 
this detail may be clearly understood, the relative dimen- 
sions of a common form of turnbuckle will be given. 

The forms and dimensions of turnbuckles vary somewhat as 
manufactured by different firms, but the form shown in Fig. 


f 









} 
\ 
| 
\ 
1 
! 
1 
I 





ee 


327 may be considered as fairly representative. The letters 
by which the various dimensions are designated are shown in 


DETAILS OF CONSTRUCTION. 991 


the figure. / is the length of the upset end, of which d is 
the diameter; 7z is the assumed distance between the two 
ends when the turnbuckle is screwed up in position upon 
them. All other dimensions relate to the turnbuckle. 

The several dimensions for this form of turnbuckle, and 
also the length of the upset ends, may be expressed in terms 
of das follows: 


E=2d+14". (200.) 
J=2d+1". (201.) 
ex=dt+h" (202.) 


Date dpa. (203.) 
sad+H". (204.) 


r=S 44. (208.) 


ae 1! 

Wi a -1 esi (206.) 
oe eal, f. (207.) 
Fo alle &. (208.) 
m= 4, (209.) 


The value of /, formula 200, is usually made a multiple 
of 4 inch, although there is no objection to giving this dimen- 
sion the exact value derived from the formula, which will 
always be a multiple of + inch. This dimension is commonly 
given values varying from 2¢d+ 2” to 2d+ 1’; a value of 
2 a+ 1%” isto be preferred. The minimum value which may 
be given to # is 4inches. Formula 200 and the preceding 
remarks apply not only to turnbuckles, but to all ordinary 
upset screw ends. 

In the expression for the value of w, formula 206, when 
d— 1} guts SP AP 
the fraction 5 + becomes negative it is simply givena 
value of zero. 

The distance 7 between the ends of the screws is variously 
taken as 3, 4, and even 5d inches; 4 inchesis a good value. 
A value of 3 inches is, however, not uncommonly assumed. 


992 DETAILS OF CONST RUGHIGR: 


It may be noticed that values of A and m, as given by 
formulas 200 and 209, will give practically the same 
relative positions and conditions of the screw endsas a value 
of 22+ 2” for #, used with a value of 3inchesfor 7. Slight 
variations in these dimensions are not of consequence, and 
any consistent rule will be found satisfactory. 


1613. The Counter Tie Continued.—Turnbuckles 
upon counters are usually placed at a distance of about five 
feet from the lower end. Asdeterminedin Art. 1519, the 
length of the tension diagonal, center to center of pz holcs, 
is 25’ 54%"; hence (see Art. 1609), the length of the counter 


. 12” + 23” 
from back to back of loops will be 25’ 5%” + a 
25' 7132", Asan error of less than ?, of an inch is of no 


consequence in an adjustable member, the allowance of =, 
of an inch for clearance of pin holes may be wholly neg- 
lected. If the portion of the counter below the turnbuckle 
is made 38’ 0” long, back to end, then, with a distance of 3 
inches between the ends, the length of that portion of the 
bar above the turnbuckle will be 25’ 7413” — 5’ 3” = 20’ 413”, 
end to back, or, with an allowance of 4 inches between the 
screw ends, the length of the larger portion of the bar will 
be 20’ 312” from back to end. 


CONSTRUCTIVE DETAILS OF THE LATERAL 
RODS. DIMENSIONS OF NUTS. 


1614. The Lower Lateral Rods; Intermediate 
Panels.—The rods in the three intermediate panels of the 
lower lateral system will be first considered. The dimen- 
sions for each of these rods are shown in Mechanical Draw- 
ing Plate; Title:, Highway .Bridgéey (Details -iVe" Piowen: 
By reference to the detailed drawing of the floor-beam (same 
title, II), it will be found that the distance between the cen- 
ters of the lateral pin holes at opposite ends of the floor- 
beam is 19’0”—2 x 82", or 2 x (8' 94") = 17’ 64”= 2104 inches. 
This distance is the lateral projection, or reach of the lateral 
rods, in each of these three panels. In the same panels the 


DETAILS OF CONSTRUCTION. 993 


longitudinal projection, or reach of each lateral rod, is equal 
to the panel length minus the distance between the centers 
of the two lateral pin holes in the same end of the beam, or 
18’ 0°— 0' 53" = 17' 62” = 2104 inches. Hence, the length 
of the lateral rod, from center to center of pin holes, is equal 
to 7210.5* + 210.25* = 297.515", or 24’ 933”. As the rod is 
adjustable, it will be sufficiently accurate to call this length 
24) 94", 

It will be, noticed that the lateral projection of the rod 
(2104 inches) and its longitudinal projection (2104 inches) 
happen to have very nearly the same values; the length from 
center to center may therefore be determined with sufficient 
accuracy for an adjustable rod by applying formula 184, 
Art. 1576, using a mean between the two projections. 


210.5 + 210.25 
‘) 


A 


The mean of the two projections is = 2100 io 





inches, from which formula 184 gives 1.4142 x 210.375 = 
297.512 inches, or, practically, 24’ 94”, as the length from 
center to center of pins. 

As proportioned in Art. 1591, all lateral pins are 14 
inches in diameter. The length of this lateral rod from 
back to back of loops is, therefore, 24’ 9$” + i ik ie 


24’ 114”. If 3 inches be allowed between the screw ends, 
the length of the longer piece of the rod will be 24’ 114” — 
5' 3" = 19’ 84” from back to end; or, if 4 inches be allowed 
between the screw ends, the length of the longer piece will 
be 19’ 74” from back to end. ‘The lengths of the loops are 
found in the manner explained for the hip verticals, and 
the diameter and length of the upset ends are obtained as 
explained in the preceding articles. 





1615. The Lower Lateral Rods; End Panels. 
—The dimensions for each lower lateral rod in the end panels 
are shown in Mechanical Drawing Plate, Title: Highway 
Bridge: Details IV, Fig. 5. One end of this lateral rod 
connects upon the lateral pin in the shoe, and, therefore, its 
length can not be determined until the position of the lateral 


994 DETAILS OF CONSTRUCTION. 


pin in the shoe has been fixed. However, as it is desirable 
to notice here the length of this lateral rod, it will be as- 
sumed that the lateral pin holes in the shoes have been pre- — 
viously located as shown in Figs. 5 and 9 of Plate III, same 
title. By reference to those figures, it is found that the 
center of each lateral pin is laterally opposite the center of 
the shoe pin and ata distance of 10,3, inches from the center 
of the chord:. From Fig..4:of «Plate Il) title:as above-m 
is found that the lateral projection of this rod is 19’ 0” — 
103,” — 82” = 17' 57,” = 209+, inches, and that its longitu- 
dinal projection is 18’ 0” —24”=17' 94” = 2134 inches. 
Hence, the*length of the rod’from centerto center or pin 
holes is equal to 4/209.063? + 213.1257 = 298.546 inches 
= 24' 1025", or, near enough for an adjustable rod, 24’ 104”. 
The length of rod from back to back of loops is 24’ 10$” + 
a eor a 25' 04”. If the shorter piece is5')0" from Dack 
to end, and the distance between the screw ends assumed 
to be 3 inches, the length of “the longer piece -willae 
25' OL" — 5' 3” = 19' 9}” from end to back; but if 4 inches 
be allowed between the screw ends, the length of the longer 
piece will be 19’ 81” from back to end. ‘The relative dimen- 
sions of the loops, screw ends, and turnbuckles have been 
fully explained. 





1616. Dimensions of Nuts.—As nuts are used upon 
the ends of the upper lateral rods, before calculating the 
lengths of the rods it will be expedient to notice briefly the 
relative dimensions of nuts. The standard screw threads 
recommended by the Franklin Institute have been quite 
generally adopted throughout the United States. 

When this thread is used, the diameter d, of: the bolt at 
root of thread, or the approximate diameter of rough hole in 
nut before cutting the thread, is given by the formula 


ad,=a—1.3 7, (210.) 


in which @ is the original diameter of the bolt and fis the 
pitch of the thread. (The pitch of the thread is equal to 
one divided by the number of threads per inch.) 


DETAILS OF CONSTRUCTION. 995 


The standard proportions for finished nuts recommended 
by the Franklin Institute are as follows: 
Thickness ¢ of nut: 


t=d— +’. (211.) 
Short diameter S of square or hexagonal nut: 
S=iid+ +,’. (21 2.) 


Diagonal Z, of square nut: 


f= 1.414 'S. (213.) 
Long diameter Z, of hexagonal nut: 
7A aa ET Bey (214.) 


In all these formulas d is the diameter of the bolt. 

In rough nuts, the dimensions ¢ and S are each + of an 
inch greater than in finished nuts. 

These proportions for nuts have not been very generally 
adopted, on account of the uncommon sizes of bar (not 
usually rolled by the mills) required to make the nut. Con- 
sequently, other standards are used for the dimensions of 
nuts. In bridge construction the standard commonly used 
for nuts is what is known as the manufacturers’ stand- 
ard. Table 42 gives sizes and weights of hexagon nuts by 
this standard. 


1617. The Upper Lateral Rods; Center Panel. 
—Referring to Mechanical Drawing Plate, Title: Highway 
Bridge: Details I, Fig. 2, it will be noticed that, in the cen- 
ter panel of the upper chord, the center of the lateral hitch 
(with reference to the rivet holes) is at the center of the 
chord, laterally, and at a distance of 8,%, inches from the 
center of the pin. Hence, the lateral projection of the 
lateral rod, between centers of the lateral hitches, is equal 
to the width of the bridge from center to center of chords, 
or 19 feet = 228 inches. The longitudinal projection be- 
tween the same points, or the distance between the two 
lateral hitches on the same chord member, is equal to 
18’ 08” — 2 x 8,3,” =16’ 8” = 200 inches, and the length of 
the diagonal between the same points is 4/228?+ 200° = 





996 DETAILS OF CONSTRUCTION. 


TABLE 42. 


SIZES AND WEIGHTS OF HEXAGON NUTS. 


MANUFACTURERS STANDARD. 














Size of of ay a Thickness| Short Long ee 
Boit. rigies of Nut. |Diameter.|Diameter.| Nits 

Inches. Inches. Inches. Inches. Inches. Pounds. 

i aif 4 i 1.01 7.1 

4 zi } 1 1.15 9.8 

5 _ B 14 1.30 14.7 

5 ay, 5 14 1.44 19.1 

5 5 3 14 1.44 22.9 

3 at 3 12 1.59 27.2 
3 at 1 i 1.73 39 
é 25 ue 18 1.88 44, 
i 25 1 13 1.88 50. 
1 us 1 13 2.02 54 
1 4 14 19 2.02 64 
14 15 iB! 2 2.31 96 
4 ee 18 Q1 2.60 134 
12 15 14 24 2.89 180 
14 1,5; 12 22 3.18 235 
12 155 12 3 3.46 300 
3 1) 15 34 3.05 370 
14 yt 2 34 4.04 460 
143 2 34 4.04 450 
QL 2 QL 38 4.33 560 
Q4 24 Q4 At 4.91 810 
Qa pe Qa 44 5.20 980 
3 Qi4 3 43 5.48 | 1150 

















DiPTAIES. OF CONSTR UG DION: JOT 


303.289 inches = 25’ 3.%”, or, near enough for an adjustable 
TOU. 20 fot. 

From Fig. 4 of the same plate the distance from the center 
(between rivet holes) of the lateral hitch and the outside of 
the 34-inch leg of the 34” x 5” angle is 2 inches, and, con- 
sequently, the length of the lateral rod from outside to out- 
side of the angles of the hitch is 25’ 31” +2 x 28” = 25’ 84”. 

From Table 41, Art. LG11, the diameter of the upset 
end, for a round rod 1 inch in diameter, is 12 inches, and 
from Table 42, Art..1616, it is known that, for a bolt, or the 
screw end of a rod, having a diameter of 12 inches, the 
thickness of the nut is 14 inches. With regard to the 
amount which the screw end of the rod should project be- 
yond the nut, no definite rulecan be given. Some engineers 
consider a projection of one inch at each end to be ample, 
but for small rods the projection given by the following rule 
is very commendable: 

Rule.—Wake the projecting end of the rod equal to the 
thickness of the nut. 

This rule is here followed. Hence, the total length of the 
lateral rod in the center panel is 25’ 84” +. 4 x 14” = 26' 24", 
as marked in Plate IV, title as above, Fig. 4. 

1618. The Upper Lateral Rods; End Panels.— 
By referring again to Plate III, title as above, Fig. 2, it is 
found that, in the end panels, the lateral projection of the 
lateral rod, between centers of the lateral hitches, is the 
same as in the center panel, or 19 feet = 228 inches, and 
that its longitudinal projection, between the same points, is 
equal to 18’ 08” — (144,"+ 83,")= 16’ 2"=—194 inches. 
Hence, the diagonal distance between the centers of the 
lateral hitches is equal to 4/228°-+ 194’ = 299.366 inches = 
24' 112”, nearly, and the total length of each lateral rod in 
the end panel of the upper lateral system is 24’ 113’+ 
2x (28"+ 14’+ 14”) = 25’ 108”, as marked upon the drawing. 
The length of the thread ends will be the same as given in 
connection with the dimensions of turnbuckles. A length 
of 44 inches, as given by formula 200, would be sufficient 
for each threaded end. 


998 DETAILS OF CONSTRUCTION: 


CONSTRUCTIVE DETAILS OF THE BEAM 
HANGER. 


1619. The Hanger Rods.—The beam hanger is 
shown in Plate, Title: Highway Bridge: Details IV, Fig. 
”. Onaccount of its form, this member isalso called a stir- 
rup. The sizeof the beam hanger is sometimes determined 
in making the general design, but it is often left to be pro- 
portioned as a detail. The total load upon each floor-beam 
is 41,200 pounds (Art. 1586) ; hence, the load upon the 
41,200 

2 
ent case, the hangers are composed of bar iron with forged 
(upset screw) ends, and the unit stress allowed upon them 
is 9,000 pounds per square inch. [See Art. 1399 (e).] 
The sectional area required for each hanger is, therefore, 
20,600 

9,000 

Referring to Fig. 7 of the same plate it will be noticed 
that the section is given by two bars, or, rather, by the two 
parts or branches of the same bar, one of which, when in 
position, will be on each side of the beam. Consequently, 
the sectional area of the bar forming the beam hanger must 


©) 


not be less than — 


hanger at each end is = 20,600 pounds. In the pres- 


= 2.29 square inches. 


2 
bent slightly from a vertical position, in that portion of the 
hanger above the top of the floor-beam, its sectional area 
should be somewhat more thanthis. A bar 14 inches square 
will give a sectional area of 1.27 square inches. This is the 
size of rod most commonly used for beam hangers in high- 
way bridges, and would ordinarily be considered sufficient 
for the present case. As, however, the bar is weakened by 
bending, a bar 14 inches square has been used. 





=1.15 isduare- inches) ee As thee pane 


1620. From Table 41, Art. 1611, it is found that the 
diameter of the upset screw end required upon a bar 14 inches 
squareislfinches. These hangers fit upon 2?” pins. Hence, 
in order that the screw ends of the hanger may pass over 
and easily clear the pin, the distance between the centers of 


DETAILS OF CONSTRUCTION. 999 


the two screw ends of the hanger should be about one-eighth 
of an inch more than the diameter of the pin plus the nomi- 
nal diameter of one screw end, or 22+ 14-4 1 = 43 inches, 
as marked in the figure. This determines the distance 
apart of the two branches of the hanger, which should be 
parallel from the bottom of the hanger to the top of the 
floor-beam. ‘The clear distance between the square bars in 
the parallel portion of the hanger is 43 — 11 = 34 inches, as 
marked. 


1621. The length of the hanger should be such that it 
may be screwed up so that it will hold the beam firmly against 
the pin plates of the intermediate post. Fig. 3 of Plate, 
Title: Highway Bridge: Details I, shows that the pin plates 
of the intermediate post extend 4% inches below the center 
of the pin ; whence it follows that the distance from the 
upper part of the parallel portion of the hanger (at the top 
of the floor-beam) to the inner side of the bend should be 
equal to this projecting length of the pin plates plus one-half 
the diameter of the pin, or 42+ 13 = 64 inches, as marked. 
This distance should always be determined and marked to 
the zuzner side of the bend, wot to the center of the pin. On 
actual shop drawings, the radius of the bend should not be 
marked, but the diameter of the pin should be given. 

The top of each upset should be about $ or ? of an inch 
above the bottom of the beam ; in the present case it is 
made 4 inch above the bottom of the beam. The amount 
which each end of the hanger extends below the bottom of 
the beam is determined by the thickness of the nuts and of 
the hanger plate, together with the amount which each 
thread end should project beyond the nut. 


1622. The Hanger Nuts.—Each end of the hanger 
should always be provided with two nuts, the principal, or 
standard, nut and a small nut called a check nut. The 
check nut should always be placed adove the standard nut. 
Hexagon nuts are generally used for hangers. ‘The size of 
the principal nut is obtained from the standard sizes given 


1000 DETAILS OF CONST RUC Eas 


in Table 42, Art. 1616, by reference to which the thickness 
of the nut for 1f inches diameter of bolt or thread end is found 
tobe2inches. The thickness of the check nut is usually # of 
an inch. Each end of the hanger should project not less 
than 1 inch beyond the nut. In the present case the hanger 
plate is of an inch thick. The length of the thread end 
will be as follows: 


Above bottom of beam, 4” 
Through hanger plate, # 
Through check nut, 3B" 
Through standard nut, 2” 
Projection, ike 


Total ap 


The length from the end of the hanger to the inside of 
bend will, therefore, be 5” + 24” + 62” = 2’ 114’, as marked. 
It is not necessary to give the exact dimensions of nuts on 
working drawings. The practice in different shops varies 
somewhat, but in most cases it is sufficient to mark the 
drawing thus: 

1k” Thread Ends. 
Standard Nuts. 
3" Check Nuts. 


Sometimes special forms of locknuts are used for hangers, 
in which case the kind of nut required should be stated on 
the drawings. 


1623. Hanger Plates.—The width of the hanger 
plate should be somewhat greater than the long diameter 
of the nuts used. Single hanger plates are generally made 
5, 54, or 6 inches in width. In determining the thickness of 
a hanger plate, the latter may be treated as a beam simply 
supported at the ends and carrying a uniform load. By 
considering the resistance of the flange angles of the beam, 
as supported by the stiffeners, and the support given to the 
hanger plate by the nuts, it will be seen that this assumption 
is well upon the side of safety, 


DETAILS OF CONSTRUCTION. 1001 
Under this assumption, the bending moment is J7 = — ES 
Oa 94, Art. 1316), and the moment of resistance, 
= — (formula Z3, Art. 1243). For a rectangular sec- 


3 


ba 
tion, /= ——, andc=4d (Table of Moments of Inertia). 


128 
Hence, for this form of section, Sf — §s qs b d* a Sod? or 
> | 


Sod? 
R= : (215.) 











in which S is the fiber stress (= S,, when X is the ultimate 
‘resisting moment), 4 is the breadth, and d@ the depth of 
section. ‘This formula expresses the moment of resistance 
of any rectangular section. 

As the moment of resistance must equal the bending 








moment, J7 = X, or, in this case, Ao = 2 oe , from which 
See a3Wi 
LSS (216.) 


In our example, WV = 20,600 pounds, / = 4? inches, 4 will be 
taken equal to 6 inches, and S (= S,) may be taken at 18,000 
pounds, the same as for pins. Therefore, the thickness of 
the hanger plate should be, 





‘3 X 20,600 x 43 


ax 18,000 x 6 Obs aly 1e 





d=V 


A plate ¢ of an inch thick has been used. By noticing the 
manner in which the lower flange of the floor-beam is sup- 
ported by the stiffeners near the beam hanger (Plate, Title: 
Highway Bridge: Details II, Fig. 4), it will be seen that, 
as a considerable portion of the load upon the beam is 
delivered directly upon the hanger nuts, the hanger plate is 
relieved of much of its stress as a beam; hence, in this case, 
a thickness of ? of an inch is probably ample. 

If the flanges of the beam are not supported by stiffeners 
reasonably near to the position of the hanger, the hanger 


1002 DETAILS OF CONSTRUCTION. 


plate should be considered as a beam carrying a single load 
concentrated at the center, in which case the quantity under 
the radical sign will be just twice as great as in formula 
216. But, in such a case, the thickness, cr theguanc- 
angles to some extent helps to make up the thickness re- 
quired for the hanger plate. The thickness, as obtained by 
formula 216, will generally be somewhat greater than the 
values commonly used. 


CONCLUDING REMARKS. 


1624. All calculations necessary for proportioning, 
according to the specifications used, the constructive details 
of the members of the bridge shown in the five plates of 
Mechanical Drawing, to which we have referred, have now 
been explained. Various small details, however, such as 
pins, shoes, rollers, bed-plates, etc., still remain to bé noticed. 
These, as well as certain features relating to the main 
members, will be considered in subsequent articles. 

Conditions and requirements for the details varying from 
those here noticed are commonly met with, and are required 
by other specifications. It should also be noticed that, 
besides the connecting details explained in preceding pages, 
many other forms of connections are often used. This 
statement applies especially to the connections for the lat- 
eral rods and struts, the portal bracing, and the floor-beam. 
It is not within the limits of this Course to compare and 
discuss the various forms of practical details. A really com- 
prehensive knowledge of these can only be acquired by 
practical experience. 

The details that have been explained are not in all cases 
the best possible for the purposes intended; but it has been 
the aim to illustrate thoroughly the application of the 
underlying principles governing the proportioning of details, 
rather than to discuss the various forms of the latter. 

The principles explained in the preceding pages apply to 
the calculations and design of details in general; and if the 
student has thoroughly mastered them, he will experience 
no serious difficulty in proportioning the details and con- 


DETAILS OF CONSTRUCTION. 1003 


nections for the members of a bridge according to any 
specifications, and in conformity with the requirements of 
approved practice. 

It is absolutely impossible to formulate any system of 
rules that will apply to all cases and conditions. The prac- 
tical designer is constantly meeting new conditions, and 
in many things he must be guided by his judgment and 
experience. 


T. I[,—2é 





DETAILS, BILLS, AND ESTIMATES. 


SHOES, ROLLERS, AND BED-PLATES. 


1625. Shoes.—For the structure shown in Mechanical 
Drawing Plates, Titles: Highway Bridge: Details I, II, 
III, IV, and Highway Bridge: General Drawing, the shoes 
are shown in Figs. 5 and 9 of Plate, Title: Highway Bridge: 
Details III. Ina shoe, the upright plates which support 
the pin are called standards or ribs. In the present case, 
the thickness of each of the two standards is 2 of an inch, 
and the clear distance between them is 9f inches. (Arts. 
1539 and 1540.) 

The lower or horizontal plate forming the bottom of the 
shoe is called the shoe plate or sole plate. Before deter- 
mining the required thickness of this plate, it is necessary 
to ascertain its required length and breadth. 

In the present case, the width from out to out of stand- 
ards is 9 +2 2=114 inches. In order that it may be 
connected to the standards by 3” x 3” angles, the shoe plate 
must, as a rule, extend somewhat more than 3 inches beyond 
each standard, which gives 114+ 2 x 3= 17} inches for the 
least permissible width of the plate. The width will be 
made 174 inches. ‘The length of the shoe plate in the roller 
shoe depends upon the number of rollers required. Conse- 
quently, before proceeding with the dimensions of the shoe, 
it will be expedient to notice the dimensions of the rollers. 


1626. Roltllers.—The rollers are shown in Fig. 7 of the 
last plate referred to. As may be seen in the figure, they 
are secured together by two bars, called side bars. The, 
turned ends of the rollers are made to run in holes drilled in 


For notice of copyright, see page immediately following the title page. 


1006 DETAILS, BILLS, AND ESTIMATES. 


the side bars much the same as the ends of pulleys or shaft- 
ing run in journals. The ends of the side bars are generally 
connected by round bars, the ends of which are riveted 
down upon the side bars, attaching them to each other. 
Such an assemblage of rollers is called a nest of rollers. 


1627. The design of the rollers is governed by item 
(¢,) of the specifications (Art. L511). According to this 
specification, the diameter @ of the roller shall not be less 
than 2 inches, and the pressure per lineal inch of the roller 


shall not exceed 500 4/d. | 
If the diameter of the rollers be assumed to be 2 inches, 


the pressure per lineal inch must not exceed 500 V2 = 107 
pounds. The vertical pressure upon the shoe is equal to 
the reaction from live and dead load (46,300 pounds) plus 
the pressure at the foot of the leeward end post, due to the 
-wind force against the upper chord, which is equal to - 
oO bax 2 y A x i ='5,100 pounds.2 Ehes total vertical 
load that can come upon a shoe is, therefore, 46,300 + 
5,100 = 51,400 pounds, requiring the aggregate length of 
the rollers available for bearing to be ee 

The constructive details generally require the length of 
the rollers to be about 1 inch shorter than the width of the 
shoe plate, or, in the present case, 174 — 1=164 inches 
long, approximately. Fig. 7 of Plate, Title: Highway 
Bridge: Details III, shows that the actual length of the 
roller, from shoulder to shoulder, is 162inches. It will also 
be noticed that grooves are turned in the centers of the 
rollers, in order that they may pass over small bars riveted 
on the bottom of the shoe plate and top of the bed-plate 
(Figs. 5 and 8, same plate). The office of these bars is to 
act as a track or guide, over which the grooves in the rollers 
may run, holding the rollers and also the shoe truly in 
position. 

In some cases these bars on the shoe plates and bed-plate 
are solid ribs formed by planing down the bearing portions 








a PO. ANCES: 


DETAILS, BILLS, AND ESTIMATES. 1007 


of the plates: In the present case the bars riveted to the 
shoe plate and bed-plate are 14 inches wide, and the grooves 
1g inches wide. As the grooves are made to clear the bars, 
the rollers have no bearing in this portion of the length, and, 
therefore, the effective or bearing length of each roller must 
be considered to be shortened 12 inches by this detail, ma- 
king the length of each roller, effective in bearing, equal to 
163 —1#=15 inches. The number of rollers required ‘is, 
"9 


(A 


therefore; equal to ea = 4.8, or, practically, 5 rollers. 





Not less than ¢ of an inch clearance must be allowed 
between each two adjacent rollers, and a clearance of 4 of | 
an inch may be used when obtainable. In the present case, 
if + of an inch clearance is used, the distance from out to 
out of the rollers will be 5 x 2+ 4x 4+=11 inches. 


1628. Coefficient of Expansion.— According: to | 
item (w,) of the specifications (Art. 1511), ‘‘ variations in 
temperature, to the extent of 150 degrees (Fahrenheit) 
must be provided for.” 

For a variation in temperature of 150 degrees (Fahren- 
heit), the amount of expansion or contraction of wrought 
iron is given approximately by the formula 


l 


—— 1,000’ (217.) 


in which e is the total amount of expansion, and / the length, 
in inches, of the piece of iron (the span of the bridge, in this 
case) considered. 

This is usually expressed as a coefficient, and is called the 
coefficient of expansion. Thus, for a variation of 
150 degrees, the coefficient of expansion for wrought iron is 
.001. For structural steels it is substantially the same. 

In the example, then, the amount of expansion (or con- 
traction) to be provided for at the roller shoe is equal to 
90 x 12 ie 

1,000 
to the width out to out of rollers, it is found that the 


= 1.08, or, nearly, Idinches. By adding this amount 


DETAILS, BILLS AND? EST IMAGE 


1008 


yz” 





17: 


2 





Scale of forces 1’=20000 lb. 
Scale of distances 3’=1 ft. 


FIG. 328, 




















DITATLUS, “BLEWUS = A0N STM APES: 1009 


required length of the shoe plate is 11 + 14 = 122 inches. 
As but a small portion of the width of each roller bears 
upon the plate, the distance out to out of the dcarings of the 
roller will be somewhat less than 11 inches, and a length of 
12 inches could have been used for the shoe plate. A 
length, however, of 13 inches is used. 


1629. Bending Moment on Shoe Plate.—It will 
be sufficiently correct to consider the pressure upon the 
bottom of the shoe to be uniformly distributed over its 
bottom surface. This will be practically correct for the 
anchored shoe, and for the roller shoe the error will be 
slight. The load upon the shoe is delivered upon the shoe 
plate through the standards. If, for convenience, we 
imagine the shoe to be inverted, we shall have, in the case of 
a shoe with two standards, a uniformly loaded beam resting 
upon two supports and overhanging each support. 

As previously determined, the maximum total load upon 
a shoe is 51,400 pounds. The load upon each standard or, 
considering the standards as supports, the reaction of each 
. 51,400 
SUpPOrt1§ — 9 
the standards, from center to center, is 9£ + 2 = 10$ inches. 

In Fig. 328 the shoe is. shown inverted, acting as a 
uniformly loaded beam upon two supports, extending 
beyond each support. The uniform load upon the beam is 
represented as divided into sections, and the weight of each 
section is considered to be applied at its center of gravity. 
Each section is 1 inch long, except the two end sections, 
which are each 14 inches long. Consequently, the weight 
upon each intermediate section is equal to ee = A;d9 6; Ol, 
practically, 2,940 pounds, and the weight upon each end 
section is 14 X 2,937 = 38,671, or, practically, 3,670 pounds, 
as indicated in the figure. (See also Art. 1171, Rule.) 

The same figure shows the force diagram and moment 
diagram for this beam. In the force diagram, the pole dis- 
tance is made equal to 30,000 pounds. It will be noticed 





= 25,700 pounds. The distance between 


1010 DETAILS, BILLS, AND ESTIMATES. 


that the bending moment in this beam is negative at the 
supports and positive in the middle portion. (It is evident 
that such a beam could project far enough beyond the sup- 
ports so that the bending moment at the center also would 
be negative. ) 

Either the positive or the negative bending moment may 
be the maximum bending moment, and, consequently, the 
maximum intercept of each character must be measured. 
The maximum negative intercept occurs at either support 
and measures —.60 of an inch, nearly; hence, the maxi- 
mum negative bending moment will be — .60 x 30,000 = 
— 18,000 inch-pounds. 

The maximum positive intercept occurs at the center f, 
and measures.76 of an inch. ‘This shows that the absolutely 
maximum bending moment occurs at this point. Its value 
is .76 X 30,000 = 22,800 inch-pounds. 

On account of the uniform load being assumed to be con- 
centrated at the centers of the various sections, this bending 
moment is slightly in excess of the true one, but it is 
sufficiently correct for all practical purposes. 


1630. The exact bending moment upon a shoe of this 
form may be easily calculated. If a beam is uniformly 
loaded over its entire length 0, Fig. 329, and the amount 7p. 


EERE LAB ra te 


ee es | 8 Ba eae 


FIG. 329. 














which it projects beyond one support is equal to the amount J’ 
which it projects beyond the opposite support, the bending 
moment J7/ at the center will be given by the formula 


W b Ws 


in which IW is the total load upon the beam, and s and 6 
have the values indicated in the figure. This bending 
moment will be positive or negative, according as the result 
is positive or negative. 


DETAILS, BILLS, AND ESTIMATES. 1011 


This formula assumes a uniform load over the entire 
breadth 4 of the shoe. When the rollers are grooved in the 
center, as in Plate, Title: Highway Bridge: Details III, 
Fig. 7, they will support no load upon the groove, and the 
bending moment at the center of the shoe, as given by 
formula 218, will be a little too large when positive, and 
too small when negative. It would be.possible to state a 
formula for such cases, but the bending moment for each 
particular case can be readily computed by applying the 
principles of moments. 

The negative bending moment — J/ at either support will 
be given by the formula 
W p° 
2b? 
in which f may represent either / or f’ of Fig. 329, for this 
formula applies whether / and 7’ be equal or unequal. 

In our case the bending moment at the center of the shoe 

17.5 


: 51,400 
is, by formula 218, ar ae (10.5 a 


~ 


ey) ee (219.) 








) = 22,488 inch- 
pounds. The bending moment at either support is (for- 


51,400 3.5° 
mula 219) —~ a 





= — 17,990 inch-pounds. 


1631. Thickness of Shoe Plate.—We have seen 
(Art. 1623) that the moment of resistance of a beam of 





nelipie et gh 
rectangular section is X= go whence, 
6A 
(7 een SF" (220.) 


In the present case the length of the shoe plate, corre- 
sponding to the total width of the beam, is 13 inches. But, 
as shown in Fig. 5 of the plate just referred to, the section 
at the center of the shoe plate of the expansion shoe (the 
position of maximum bending moment) is reduced by three 
rivet holes. 

By considering the diameter of each rivet hole to be 4 of 
an inch greater than the diameter of the undriven rivet, 


1012 DETAILS, BIULS, ANDEESTIMAr ir: 


the width to be deducted for the three rivet holes is 
3 xX 3 = 21 inches, making the net length of the shoe plate, 
acting as the effective width of the »beam, equal to 
13 — 21=10% inches= 6. As the load is somewhat dis- 
tributed, and the shoe plate materially supported and 
strengthened by the horizontal legs of the angles forming 
the standards, the value of S may be taken at 18,000 
pounds, the same as for pins. By substituting the values 
of Rk, S, and din formula 220, we get, for the thickness of 
6 & 22,800 


the shoe plate, d= 18,000 x 10.75 = .84, or, nearly, £ of 








an inch. 

There are no rivet holes to be deducted from the section 
at the center of the shoe plate of the anchored shoe, and, 
consequently, the value of 6 for this shoe is 13 inches, and 
aay ane =),76. 01, practicalhyije-2Ot .Aneancil wees 
thickness of ~ of an inch, however, is used for the shoe 
plates of both the roller and the anchored shoes. It is to 
be noticed that, for the roller shoe, the rollers and bed-plate 
may be considered to act somewhat as beams, thus assisting 
the shoe plate sufficiently to make up for the section cut out 
by the rivet holes. This being the case, a thickness of 3” 
would probably be sufficient for the shoe plates of both 
anchored and roller shoes. 

The standards or ribs of the shoe must be given such form 
as will clear the upper flanges of the channels of the end 
post. For bridges of moderate span the form of the stand- 
ards is commonly made symmetrical with reference to a 
vertical line through the center of the pin hole. In many 
shoes the horizontal legs of the angles forming the stand- 
ards are turned outwards, and the smaller angles (in the 
present case, 3” x 3” xX 2" angles), connecting the vertical 
legs of the larger angles to the shoe plate, are omitted. 
Sometimes, also, each standard consists simply of a vertical! 
plate, connected to the shoe plate by a single angle. The 
standards shown in Plate, Title: Highway Bridge; Details 
III, Figs. 5 and 9, are very substantial. The two shoes 





DETAILS, BILLS, AND ESTIMATES. 1013 


there shown are alike, with the exception of the small guide 
bar on the bottom and the connection for the shoe strut on 
the roller shoe, and the holes for anchor bolts in the anchor 
shoe. 


1632. Another Form of Shoe. 





Although the form 


of shoe shown in the plate just referred to is commonly 
used for bridges of moderate span, other forms are often 
used, <A form of shoe similar to that shown in Fig. 330 is 


























Fic. 330. 


used for long and heavy spans. A side elevation and rear 
elevation of the shoe are shown, and also a side elevation of 
the lower end of the end post, with a section on the center 
line of the same. 

In this shoe the bearings of the end post upon the pin are 
so nearly opposite those of the shoe standards as to produce 
but a comparatively small amount of bending moment in 
the pin. The standards of the shoe are supported lateraily 
by a plate corresponding to the cover-plate of the end post. 
The rollers are held in position by angles attached to the 


1014 DETAILS, BILLS, AND ESTIMATES. 


shoe plate, thus allowing the accumulations of dirt on the 
bed-plate to be cleaned out between the rollers. The 
anchorage is given by anchor bolts passing through slotted 
holes in the shoe plate. 


1633. The Bed-Plate.—The bed-plate is shown in 
Plate, Title: Highway Bridge: Details III, Fig. 8. Item 
(v,) of the specifications (Art. 1511) requires all bed- 
plates to be of such dimensions that the greatest pressure 
upon the masonry shali not exceed 250 pounds per square 
inch. This condition, together with the dimension of the 
shoe and rollers, determines the size of the bed-plate. In 
the present case, as determined for the shoe, the total load 
upon the bed-plate is 51,400 pounds, and, consequently, the 
bed-plate must have a bearing surface upon the masonry of 
51,400 
250 
long as the shoe plate and should generally be somewhat 
longer; in the present case it is made 14 inches long. 
Hence, the width of the bed-plate necessary to give the 

205.6 


required bearing upon the masonry is aE ce 143 inches, 





— 205.6 square inches. The bed-plate must be as 


nearly. 

Item (wz,) of the specifications requires that ‘‘ while the 
roller ends of all trusses must be free to move longitudinally 
under changes of temperature, they shall be anchored 
against lifting or moving sideways;” consequently, at the 
sides of the bed-plate, outside of the rollers and shoe, there 
must be upright pieces, the tops of which extend inwards 
over the edges of the shoe plate, or some equivalent arrange- 
ment, to prevent the shoe from lateral movement or lifting. 
As these side pieces can be most advantageously formed of 
pieces of angles or Z bars (also written zee bars), of which 
the horizontal legs attaching to the bed-plate must be 
turned outwards, the bed-plate will usually be required to be 
about 6 inches wider than the shoe plate. In the present 
case the bed-plate is made 24 inches wide. Its bearing 
surface upon the masonry is, therefore, uty Je in excess Rs 
the bearing surface required. 


DETAILS, BILLS, AND ESTIMATES. 1015 


1634. By reference to Figs. 7 and 8 of the same plate 
(III), it will be seen that each end of the bed-plate projects 
Pree ais or, near enough f é 

9 = 34%, OF, g or present purposes, 3.8 
inches beyond each end of the rollers. The pressure upon 
the bottom surface of these projecting ends produces a 
bending moment in the bed-plate at the ends of the rollers, 
51,400  3.8° 

2X 24 
219). The thickness of the bed-plate must, therefore 


6 15,463 . 
(formula 220), be V - RN Ae es .61 of an inch, or say 2 


8,000 x 14 — 


whose value is 





= 15,463 inch-pounds (formula 





of an inch. 

This assumes the pressure upon the bottom of the bed- 
plate to be uniformly distributed over its surface. But, as 
determined above, the limit of the pressure allowed upon 
the masonry requires a width of only 14? inches for the 
bed-plate, which is less than the bearing length of the 
rollers. Hence, the entire pressure upon the bottom of the 
bed-plate may be considered to be applied upon that portion 
of its width between the ends of the rollers, assuming no 
pressure upon the projecting ends, in which case there will 
be no bending moment. 

As shown in the figure, a piece of 3” x 4” x 3” x §” Z bar 
is riveted upon one side of the bed-plate in such manner 
that the upper horizontal leg of the bar will extend inwards 
over the edge of the shoe plate. This leg of the bar is cut 
off sufficiently to clear the heads of the rivets in the shoe 
plate. On the opposite side of the bed-plate, a 3” x 3" x 2” 
angle is used with a small piece of 3” x 2” angle riveted to 
one end in such manner that one leg of the latter will 
extend over the edge of the shoe plate. The piece of 3” « 2” 
angle can not be riveted to the opposite end of the 3” x 3” 
angle because it would so interfere with the connection of 
the shoe strut as to prevent the shoe being placed in posi- 
tion upon the bed-plate. Consequently, at one end of the 
3” x 3” angle, a small bent anchor plate is made to serve 


the purpose of anchorage against lifting. This plate con- 


1016. DETAILS, BILLS, AND ESTIMATES: 


nects upon the anchor bolt and is detachable; it is shown 
between Figs. 8 and 9, on Plate, Title: Highway Bridge: 
Details III. 


1635. Anchor Bolts.—Item (v,) of the specifications 
requires that for trusses the anchor bolts shall not be less 
than 1+ inches in diameter. It is the general, practice to 
use two anchor bolts to each anchored shoe and to each bed- 
plate, placing each bolt at the center of the side or flange, 
corresponding to the position of the anchor bolt in the outer 
(upper) side of the anchor shoe, Plate, Title: Highway 
Bridge Details Lily Bigg: 

In the present case, however, it was found more conve- 
nient to use three 1-inch anchor bolts in each anchored shoe 
and in each bed-plate. 

In fixing the sizes and positions of the holes through the 
shoes and bed-plates for the anchor bolts, liberal clearance 
should be allowed in the holes, and their positions should be 
such that the nuts will sufficiently clear the upright pieces. | 
By reference to Table42) Arto (G1G,1tisioundthaceton: 
bolt 1 inch in diameter, the long diameter of a hexagon nut 
is 2.02 inches. Hence, the center of the bolt hole should be 
at least 14 inches from the nearest vertical piece in the shoe 
or bed-plate. In the bed-plate (Fig. 8, same plate), the 
center of each hole for the anchor bolt is 1} — 2 = 14 inches 
from the nearest side of the vertical leg of the Z bar, and 
1g — 2—%= 1} inches from the vertical portion of the bent 
anchor plate. In the shoe, the centers of the holes for the 
anchor bolts are at a distance of 13— 2= 12 inches from 
the vertical leo of the 3” x 3” angle. 

The anchor bolt is shown in Fig. 6, same plate. The 
thread end is the same as that of an ordinary bolt, but at 
the opposite end, instead of having a head, the end of the 
bolt is split to receive asmall wedge, as shown. ‘The anchor 
bolt is set in the following manner: A hole being drilled in 
the masonry, the wedge is started into the split in the bolt 
sufficiently to hold it in position, then the bolt is placed in 
the hole and driven down over the wedge, thus forcing open 





DETAILS, BLELS= ANDABSTIMATES: 101 


the split and spreading the lower cnd of the bolt. The bolt 
being placed in its proper position, the hole is filled with 
melted sulphur or lead, or with neat Portland cement mortar, 
which, when it has hardened or set, firmly holds the bolt in 
place. The form of anchor bolt shown in Fig. 6 (same plate 
as above) is called a wedge bolt. It is the best form of 
anchor bolt, though not the cheapest. 

In Fig. 331 are shown three other forms of anchor bolts 
commonly used for bridges. The form shown at a is called 
arag bolt, or swedged bolt, 
and the same names are some- 
times applied rather indiscrimi- 
nately to the form shown at J, 
though this may be more prop- 
erly called a barbed bolt. 
The form shown at ¢ is simply 
a threaded bolt. These forms 
of anchor bolts are generally 
set into the masonry about 6 
inches. If it is necessary for 
an anchor bolt to take direct 
tensile stress, as at the bottom 
of a high tower, it is usually made long with a head at the 
lower end carrying a large washer or plate, and is built into 
the masonry a sufficient depth so that the weight of the 
masonry above the head and plate will resist the tension 
upon the bolt. 





FIG. 331. 


CHORD PINS, PIN NUTS, COTTER PINS, AND 
PIN WASHERS. 


1636. The Chord Pins.—The chord pins are shown 
iy) Plate, “litle; Hiohway -Bridge: Details IV, Figs. 9,10, 
and 11. The diameters required for the pins have been 
determined in previousarticles, and only the required lengths 
of the pins and the dimensions of the thread ends and nuts 
remain to be determined. 


1018 DETAILS, BILLS, AND ESTIMATES. 


1637. Grip of Pins.—In a chord pin, the length G, 
Fig. 332, is called the grip of the pin. Thegrip of.a chord 
pin may be determined by the following rules: 











Ric dacaastactlatne hii 








G 


Verne ee emer 
FIG. 382. 


Rule I.—/f the outer dimensions of the member through 
which the pin passes are fixed, the grip will be equal to the 
net width of the member plus a constant c. 

W.—/f the pin passes through chord bars only, or chord 
bars packed outside of a riveted member, the grip will be 
equal to the net width plus >}, of an inch for each chord bar, 
and plus + ofan inch for cach riveted member ; but the total 
amount added should never be less than the constant c. 

For the value of the constant c, the practice varies. The 
value of this constant, as determined by any oneof the three 
methods indicated below, will be found satisfactory. 


(1) for all chord pins : 
aie a (221.) 


(2) For chord pins having diameters 


Less than 8 inches : c= }’. (222.) 
From 8 to 6 inches : rae A (223.) 
Greater than 6 inches: c = 3". (224.) 


(3) Lor chord pins of any diameter D: 


pols W 
ai 4”, (225.) 

In using the last formula, the value of c may be taken to 
the nearest sixteenth of an inch. 

In practice, however, when the grip of the pin, as esti- 
mated by any one of the preceding formulas in connection 
with either of the above rules, contains a fraction smaller 


6 


DE PATS, BIPUSe AND: ESTIMATES, 1019 


than one-eighth of an inch, the fraction should be called 
one-eighth. 

The amount added to the net width of the member or 
members, to obtain the grip of the pin, is to insure the fin- 
ished portion of the pin passing entirely through the mem- 
ber, making allowance for probable variations in width. <A 
perfect bearing is thus obtained for the pin, which is an 
essential condition. The practice indicated by formula 
221 is the most simple, but that indicated by formula 225 
isthe most satisfactory. In determining the grip of the 
chord pin shown on Plate, Title: Highway Bridge: Details 
IV, formula 221 was used. 

Thus, the distance out to out of the standards of the shoe 
(Plate, Title: Highway Bridge: Details III, Fig. 5) is 9% + 
2 X= 11g inches. In compliance with rule I, using for- 
mula 221 for the value of c, the grip of the shoe pin is 
made equal to 114 +4=11% inches. (Plate, Title: High- 
way Bridge: Details IV, Fig. 9.) The diameter of the pin is 
2% inches. Hence, if the value of c were taken according to 
formula 222, the grip of the pin would be 1144+14=112 
inches. If formula 225 were used, the value of c would be 
ae — xs of an inch, and the estimated grip of the pin 
would be 114+ = = 11,8, inches, while the practical grip of 
the pin would be 112 inches. 


1638. Screw Ends and Pilot Nuts.—As shown in 
Fig. 332, the screw ends of chord pins are turned down 
smaller than the main portion of the finished pin, in order 
that they may pass through the pin holes easily and without 
injury to the threads. This, of itself, would require the 
screw ends to be but slightly smaller than the body of the 
pin, but it has been found desirable to make each screw end 
of a pin enough smaller than the body, or finished portion, 
to permit a dome-shaped nut, finished to the same diameter 
as the pin, to be screwed upon the end. ‘This nut serves to 
facilitate the process of entering and driving the pin through 
the various members which it connects, and also to protect 

T. [1,—26 


1020 DETAILS, BILLS, AND ESTIMATES. 


the threads of the pin during the process. Such a nut is 
known as a pilot nut or pin pilot. A pilot nut is shown 
in Fig. 333, from which its form 
will be readily understood. 

For the dimensions of the screw 
ends of chord pins, as relating to 
the finished sizes of the pins, the 


? 
practice varies considerably. As 
a rule, each bridge office adopts 
and uses such dimensions of 


RAE ik screw ends as satisfactorily fulfil 
the requirements of its shop practice, and thus forms a stand- 
ard of its own. The dimensions of screw ends given by 
the following formulas, however, will be found satisfactory ; 
they probably represent the average practice. 





Diameter of screw end: 
Hey | (ORES 
Length of screw end: 
a Genie (227.) 


In these formulas J is the diameter of the finished pin; d 
is the diameter of the screw end to the nearest eighth of an 
inch, and eg is the length of the screw end to the nearest 
sixteenth of aninch. (See Fig. 332.) 

Thus; for the shoe. pin (Plate, “Title: Hichwaysbrdoe. 
Details IV, Fig. 9), the diameter d of the screw end is 3 x 
23 = 33, or, practically, 2inches. The length e of the same 
is 2-++ 1 = 14 inches. 


1639. The Diameters of Finished Pins.—It will 
be well to notice here the practice with regard to the diam- 
eters of finished pins, which varies in different shops. Round 
bars of diameters greater than 1,% inches are not commonly 
rolled in sixteenths. As rolled, the diameters of round iron 
greater than 1,% inches are nthe of 4 of an inch. 

In finishing the pin, it is the ese tse) of some shops to 
turn off 4 of an inch, 1, e., to make the diameter of the 


DETAILS, BILLS, AND ESTIMATES. 1021 


finished pin $ of an inch less than the diameter of the rolled 
bar, while in other shops the practice is to turn off only ;, 
of an inch in finishing the pin. The former practice gives 
excellent results, but is not economical. The latter practice 
is economical, but it does not in every case produce a well- 
finished pin. 

It is evident that by the former practice the diameter of 
the finished pin, if greater than 1,4 inches, will always be a 
multiple of $ of an inch, while by the latter practice the 
diameter of the finished pin, if greater than 14 inches, will 
always be in odd sixteenths of an inch. 

Most bridge offices adopt a standard minimum size of pins, 
and use no pins for any purpose having diameters less than 
the minimum size adopted; 1? inches is a standard minimum 
size often used for the diameters of pins, and will be adopted 
in this Course. 


1640. The Pin Nuts.—As now quite generally made, 
pin nuts have recesses on the inner sides to admit the end or 
shoulder of the finished portion of the pin. This form of 
pin nut, known asa recessed nut, is shown in Fig. 334. 
Before recessed nuts came into use, washers fitting over the 
ends of the pins were used in connection with flat nuts; they 
are still used, but not extensively. The first recessed nut 
which appeared on the 
market was a pressed 
wrought-iron nut, known 
as the Lomas nut. This — 
was a patented nut; it was 
somewhat similar in form |Y 
to the nut shown in Fig. 
334, and was at one time 
widely used. The name 
Lomas nut is sometimes in- 
discriminately applied to 
any recessed nut. A mal- 
leable iron recessed nut, 
which seems to be satisfactory, is now much used. Its 






FIG. 334. 


1022 DETAILS, BILLS, -ANDSE> Ti GE: 


general form isshown in Fig. 334. It isunnecessary to give 
here the exact dimensions of this nut, which vary somewhat 
irregularly in the different sizes, but for convenience the 
following approximate dimensions may be given with refer- 
ence to J, the diameter of the finished pin. See the figure. 


Diameter d, of rough hole for screw: 


3 


‘do D— =f. (228,) 
Diameter R of recess: 
RD nen 20%) 
Short diameter S of nut: 
Steins af (230.) 


Long diameter L of nut: 
Bab ee: (231.) 
Length t of thread: 
3 ity. 


Depth r of recess: 
12 meagre 
Total thickness T of nut: 
9) Me heap 


In applying formulas 226 to 234, inclusive, the diam- 
eter DY of the pin should contain no fraction smaller than 
4+ inch; if the actual diameter of the pin contains a smaller 
fraction, the full quarter inch next above should be used. 

Values from these formulas will be obtained to the nearest 
sixteenth of an inch, except formulas 226 and 228, for 

* This is correct for 7 threads to the inch, and may be considered 


near enough for 8 and 6 threads to the inch, which are the sizes of 
threads commonly used for pin nuts. 


DETAILS, BILLS, AND ESTIMATES. 1025 


which the values will be obtained to the nearest eighth of 
an inch. It will be noticed that the length of the thread, 
as given by formula 232, will be in all cases 4 inch less 
than the length of the screw end of the pin, as given by 
formula 2273 which may be expressed in the form 

a es 

ots 

It is not necessary to give the dimensions of pin nuts on 
shop drawings (or shop lists); it is usually sufficient to give 
the required dimensions of the pins and state the kind of 
nut required. 


_ 1641. Cotter Pins.—Pins of the form shown in Plate, 

Title: Highway Bridge: Details IV, Fig. 12, are: called 
cotter pins. They are often used for lateral pins and for 
certain other purposes, but are not commonly used when 
the diameter of the pin is greater than about 3 inches. In 
general form, a cotter pin is somewhat similartoa bolt. It 
usually has a round (cylindrical) head, and at its opposite 
end, instead of having threads cut, it has a hole drilled to 
receive a small split pin formed by bending a piece of half 
round iron, so the flat sides will be in contact. 

The split pin so formed is sometimes called a key, but it 
is more commonly known as a cotter. The end of a cotter 
pin is tapered slightly in order that it may be more easily 
inserted into the pin hole. 


| 
| 
| 


FIG. 335. 


A cotter pin is shown in Fig. 335. The relative dimensions 


1024 DETAILS, BILLS, AND ESTIMATES. 


of cotter pins given by the following formulas will be 
in accordance with good practice, each result being taken to 
nearest sixteenth of aninch. See the figure. 


Thickness T of head: 


Diet, 
Diameter H of head: 
he Be PAE If (236.) 
Length C of cotter: 
Gee ee a (237.) 


Diameter or width c of cotter: 
Caan Lie (238.) 
Diameter h of cotter hole: 


1, 
=e = 16 : CRED 
Diameter d of end: 
d= D, 240.) 
Length e of end: 
3 1 ” 
Fae Dore (241.) 


Length t of taper: 


Poe (2 


Total length L of pin: 
d beret 6 PSY (243.) 
In these formulas / is the diameter of the finished pin. 
1642. The grip of a cotter pin is determined substan- 
tially the same as for a chord pin, but formula 222 should 


generally be used for the value of the constant. 


DETAILS, BILLS AND ESTIMATES: 1025 


The grip of acotter pin should always be given from the 
under side of the head to the tnner (or nearest) edge of the 
cotter hole, as shown at G in Fig. 335. 

The preceding formulas represent practical and economi- 
cal dimensions for cotter pins, but as the diameter and grip 
are the only really important dimensions of a cotter pin, 


slight variations in other dimensions are not of conse- 
quence. 


EXAMPLE.—For a cotter pin having a diameter of 1% inches, and a 
net grip of 24 inches, what are the remaining dimensions, as given by 
the preceding formulas ? 


tte Bee 


SoLUTION.—Thickness of head, 7 = me a z= 3 
Diameter of head, ffm A$ Ae 2 == OH. 
Length of cotter, C=14x1#+ 4=24". 
Diameter of cotter, Gs) <1. 
Diameter of cotter hole, Z= §++74,—,%". 
Diameter of end, @=°4xX%18=17". 
Length of end, eé= #X1#+ =f’. 
Length of taper, f= +X 4=7%". 
Length of grip, G=24+ += 23". 
Total length of pin, L=2¢+ 84+4=4". 


1643. Pin Washers.—In Plate, Title: Highway 
Bridge: Details III, Figs. 10 to 13, are shown small rings 
of sizes to fit loosely upon the pins. They are used to fill 
the vacant places between the various members connecting 
upon certain pins, and serve to hold the members in their 
proper positions. These rings are known variously as pin 
washers, packing rings, and filler rings. They are, 
as a rule, formed by bending strips of metal into circular 
form so that the inside diameters will be about 4 of an inch 
greater than the diameter of the pins. The metal used is 
from 5%; to $ inch thick. 

In determining the lengths of pin washers, sufficient 
clearance must be given, making ample allowance for vari- 
ations in the thickness of the members. If this is not done, 
and the pin washers do not fit readily into place, they are 
very liable to be omitted in the process of erecting the 
bridge. In determining the lengths of the pin washers. 


1026 DETAILS, BILLS, AND ESTIMATES. 


practically the same allowances are made as in rule II, 
Art. 1637, for determining the grip of the pin. 


EXAMPLE.—What should be the length of the pin washer for the 
hip joint of the bridge shown or the Mechanical Drawing plates? 


SoLuTION.—The distance between the inner surfaces of the pin 


: vi ; 
plates on the end post at the hip joint is 72 —2 x 16 64inches. See 
Plate, Title: Highway Bridge: DetailsI, Fig.1. By allowing 4 of an 
inch on each side for the riveted member and ;% of an inch for each 


forged bar, the length of the pin washer will be 64— 2x vie 4x : ~~ 
4x a2 inches. Ans. See Plate, Title: Highway Bridge: Details 
III, Fig. 10. 


1644. The Shop Drawings.—The details of the 
members and their various connections, as shown in Plates, 
Titles:»: Highway Bridge: Details lee isi eco er ies 
with the calculations necessary for proportioning the same, 
have now all been explained. In the order of procedure for 
the construction of the bridge, the shop drawings may be 
considered to be completed, 

It will be well, however, to notice that, in many cases, 
sizes and dimensions which, in the plates referred to, are 
shown marked as dimensions, are usually simply stated in 
actual working drawings. ‘The sizes of all plates, bars, and 
shape iron should be distinctly stated upon the drawings, 
and such dimensions as will be clearly understood from such 
statement may be omitted. Thus, for the main tie bar, 
Plate, title as above, IV, Fig. 1, the marked dimensions 
2”, 18", 5£", 6", and {” would usually be omitted in the draw- 
ng, but under the drawing would be written: 

13 ue 


Main Tre Bar, 2" x —",; Heads, 5%" x 3 


16 , 8 required. 


This statement gives all necessary information concern- 
ing the main tie bar, except the sizes of the pin holes and 
the length from center to center of the same. 

Shop drawings, and, indeed, nearly all bridge drawings 


DETAILS, BILLS, AND ESTIMATES. 1027 


are made upon tracing muslin, in order that they may be 
blue-printed. The drawing is usually made in pencil on 
detail paper, then traced and finished in ink on the tracing 
muslin. As many blue-prints should be taken as are 
necessary for the office and the different shops. 





BILLS. 


SHOP LISTS. 


1645. What is stated above concerning the main tie 
bar is true also of many other members; in fact, it is true 
of nearly, if not quite, all forged members. Therefore, 
instead of showing such members upon the shop drawings, 
it is the practice in most bridge offices to state the necessary 
dimensions upon certain blank forms or sheets, thus con- 
veying the same information with much less labor. Such 
sheets are commonly known as shop lists. The fol- 
lowing will serve to illustrate the general forms of shop 
lists. Two somewhat different forms are given for eye- 
bars. 

It will be noticed that lists (4) to (£), as filled out, give 
all necessary information concerning the forged members 
shown in Plate, Title: Highway Bridge: Details IV, Figs. 
1 to 6. In these lists are given in each case, not only 
the dimensions of the finished bar, but in the column 
headed Ordered Length is also given the length of the 
rolled bar necessary to give the required finished dimen- 
sions. 

This feature of the shop lists will be more fully explained 
in the following articles. For the student’s convenience, 
the figure to which each item refers is designated in the 
left-hand column. Lists (A) and (4) are simply two differ- 
ent forms which serve the same purpose. 

It will be noticed that, in stating the lengths back to end 
in list (D), 4 inches are allowed for the distance between 
the two screw ends, according to the practice indicated in 


DETAILS, BILLS, AND ESTIMATES. 


1028 








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DETAILS, BILLS, AND ESTIMATES. 








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FORGE LIST. 


DETAILS, BILLS, AND ESTIMATES. 1031 


Sheet No. os 


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Art. 1612. The lengths 
of upset ends given in lists 
(D) and (£) are also in ac- 
cordance with the practice 
there indicated. 

For the details of pin-con- 
nected members, the practice 
in some bridge offices is to 
indicate the size of each pin 
hole by stating the size of the 
pin, allowance for the clear- 
ance of the pin hole being 
made in the shop. In other 
bridge offices the practice is 
to state the exact diameter 
actually required for each 
pin ole. Each practice has 
its advantages. 

Either system will obtain 
the required results if con- 
sistently followed, but the 
latter practice is to be pre- 
ferred. On the Mechanical 
Drawing plates and in the 
shop lists given above, the 
former practice has been fol- 
lowed, except in list (4), in 
which the diameter of the 
pin hole is stated. 

In lists (/’) and (G) is given 
all necessary information 
concerning the pins shown 
in Plate, Title: Highway 
Bridge: Details IV, Figs.9 to 
12. In list (7) the lengths 
of all screw ends are given 
according to formula 227. 
In list (G), all dimensions of 


DETAILS, BILLS, AND ESTIMATES. 


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1034. DETAILS, BILLS, AND ESTIMATES. 


the cotter pin are according to the formulas given in Art. 
1641. For the details of pins, the correct diameters of 
the finished pins are always stated. 

The forms of shop lists, as used in the different bridge 
offices, of course vary somewhat, but the forms given serve 
to illustrate the general system. The blank forms for shop 
lists are generally printed upon tracing muslin or upona 
thin bond paper which will blue-print. 


IRON ORDER. 


1646. General Method of Procedure.—After the 
shop drawings are completed, the next step in the process of 
the construction is to make out the iron order. The com- 
panies who manufacture bridges do not usually roll the iron 
themselves. A few of the larger bridge companies own 
both rolling mills and construction shops, but even in such 
cases the management of each is generally separate and 
distinct from the other. 

The greater portion of the material for each bridge is 
ordered from the rolling mill in the exact lengths required, 
making due allowances for the requirements of manufacture. 
There is, practically, no waste in such ordered material, 
beyond that necessary to finish it properly. 


1647. Certain common sizes of channels, angles, plates, 
and bars are carried in stock by most bridge works. Stock 
iron is ordered in lengths of 30 feet. For iron rolled in 
lengths greater than 30 feet the prices per pound are some- 
what higher. This fact should be borne in mind in making 
the design for a metal structure; the lengths used should 
generally not be greater than 30 feet. A list of the material 
carried in stock, called the stock list, should always be 
kept in the office, and the material checked off as used. 

From the shop drawings, a list of the material required to 
make the -various members of the structure is made out. 
In this list, the material is taken in substantially the same 
order as it appears upon the shop drawings. This list is 
known as an order list. 


DETAILS, BILLS, AND ESTIMATES. 1038 


The order list is then carefully scrutinized and compared 
with the stock list, and such sizes as are carried in stock are 
marked to be taken from stock. When this is done, a 
second list is made, in which the remaining pieces, not car- 
ried in stock, are grouped and classified, the various pieces 
of each size and shape being assembled together. In this 
classification, the channels are usually written first, followed 
by the angles or other shape iron, then by the plates, flat 
bars, square bars, and round bars, respectively. In this 
list, also, the lengths of short pieces of plates or bars of the 
same size, such as pin plates, batten plates, etc., are usually 
added together, and the aggregate length given in one or 
more pieces. In such case, the length of each piece thus 
formed must not be more than 30 feet. This classified list 
of the material to be ordered is called the iron order. 
It is made out by the engineering department of the bridge 
works, and then transmitted to the business department, by 
whom the actual order is placed with the rolling mill. 


1648. Ordered Lengths of Material.—In making 
out the order list for the material for a bridge, certain rules 
must be observed with reference to the ordered lengths of 
the material. 

Pieces of plates, bars, angles, or other shapes, which are 
not required to be finished to exact lengths, or to be upset, 
welded, or forged, are ordered in neat lengths, that is, in 
the lengths actually shown on the drawings, without any 
allowance for extra length. When a number of short pieces 
of the same size are required, however, a single plate, hav- 
ing a length equal to the aggregate length of all such plates, 
is usually ordered. 

When short pieces of plates are to be cut diagonally, or 
on a bevel, they are usually ordered in such rectangular 
lengths as will best cut to the required dimensions. 


1649. If one or both ends of a rolled or built member 
are to be planed, in ordering the material a certain amount 
must be added to its finished length, to provide for the 
material taken offin planing. This amount varies somewhat 

LT. ll.—2&7 


1036 DETAILS, BILLS, AND ESTIMATES. 


with the form of the planer used; but with the machines 
commonly used in bridge shops, the amount to be added for 
each finished end should generally be as follows: 

Tf the greatest dimension (width) of the member does not 
exceed 6 inches, add } of an inch. 

Tf the greatest width of the member exceeds 6 inches, add 
lg of an inch for each additional 6 inches width, or fraction 
thereof. 

This may also be expressed by the following formula: 


1 b 
4 TR Re (244.) 


in which a is the length to be added for each finished end, 
6 is the width of the member in inches, and ¢ is a constant 
which, for most planers, may be taken at ;, of aninch. In 


ioe. eee 
this formula, any fraction in the value of the expression r; 


should be considered as unity. 


1650. In ordering the material for eye-bars, upon which 
the heads are to be formed by piling and forging, the length 
of bar required beyond the center of the pin hole is given 
for one head by the formula 


vee wv 
a=5—-(F+e) (248) 


in which a is the additional length of bar beyond the center 
of the pin hole, // is the diameter of the head, wis the width 
of the bar, and c is a constant, which may usually be taken 
equal to # of an inch. This formula applies generally to 
wrought-iron eye-bars. 

The additional length a of the bar beyond the center of 
the pin hole, required to form one eye-bar_head by upsetting 
and forging, is given by the formula 


a=3(H—w)+te, (246.) 


in which /7 is the diameter of the head, w is the width of 
the bar, andc is a constant, which must be obtained from 
the practice of each shop, but may usually be taken equal to 


DETAILS, BILLS, AND ESTIMATES. 1037 


ay 
3— +e This formula applies to steel eye-bars as generally 
manufactured. 

The additional length @ beyond the center of the pin, 
necessary to form one welded loop upon the end of a round 
or square bar, is given by the formula 


a=3.57 D+ 4.57 d+, (247.) 
in which / is the diameter of the pin, @ is the diameter of 


the round, or the side of the square bar, and ¢ is aconstant, 
which wiil here be taken simply equal to zero. 


1651. The additional length ~ necessary to form one 
upset upon the end of a round bar is given by the formula 


u= (3 es 1) jas Sp (248.) 


in which PD is the diameter and £ the length of the upset 
end, d@ is the diameter of the original bar, and ¢ isa constant, 
which may usually be taken at # of an inch. 

The additional length w necessary to form one upset upon 
the end of a square bar is given approximately by the 
formula 


w= 185. (=; ~121) +e, (249.) 


in which SS is the side of the square bar, ) and # have the 
same values as in formula 248, and ¢ is a constant, which 
may usually be taken as 1 inch. 

Results obtained by formula 249 are not generally as 
satisfactory as those obtained by formula 248, It is in all 
cases roughly approximate to take the length required to 
make each upset end as equal to the length of the upset. 


1652. If ordered cut tothe required length, the ordered 
length of a chord pin may be the sameas its finished length, 
as obtained by formula 227 and the preceding rules. This 
length will be given by the formula 


TAGE ate (250.) 


1038 DETAILS, BILLS, AND ESTIMATES. 


in which Z is the length, G is the total calculated grip, and 
Dis the diameter of the pin, while cis a constant, which, 
for lengths of screw ends as given by formula 227, will be 
equal to 2 inches. If all pins of the same size are ordered 
in one piece of a length sufficient to be cut into the required 
lengths, the value of c will be 4 of an inch greater, as will 
be hereafter noticed. 

The ordered diameter of a chord pin greater than 1,5 
inches must always be a multiple of 4 of an inch. The 
ordered diameter will be at the full eighth of an inch greater 
than the diameter required for the finished pin. (See Art. 


1639.) 


1653. Rivets are made with one head; the second head 
is formed in driving. For the proportions of rivet heads 
given in Mechanical Drawing, the length of the rivet before 
driving, allowing sufficient additional length for forming 
the head in driving, should be : 


For round heads: 


l=14;G+1¢¢+.6. (251.) 
For countersunk heads: 
ad 
= ligG+s +e, (252.) 


In both of these formulas, 7is the length from the under 
side of the head: tothe end of the rivet before driving 
the diameter, and G is the net grip of the rivet, while cisa 
constant which may generally be taken at 2 of an inch. 

These formulas apply to machine-driven rivets in punched 
(unreamed) holes, and will be found generally satisfactory. 
As the additional length of rivet required to make the head 
is affected by the power used in driving and by the size of 
the die or cup used to form the head, both of which vary in 
different shops, it will in some cases be found necessary to 
use a different value for c. 

For hand-driven rivets, no satisfactory formula can be 
given. The additional length of rivet necessary to form 
the head will differ in hand riveting done by different men, 


DETAILS, BILLS, AND ESTIMATES. 1039 


and the proper amount to allow for this purpose can be 
learned only from experience. 

Formulas 251 and 252 give fair approximations, and 
will be adopted here. 

In stating the lengths of undriven rivets, fractions smaller 
than eighths of an inch are not commonly used. 


1654. If a lattice bar is connected by a single rivet at 
each end, the total or ordered length Z is given by the 
formula 

L=ltwte, (253.) 
in which / is the length from center to center of rivets, w is 
the width of the bar, and ¢ is a constant, which has usually 
different values for different widths of bar, and also in differ- 
ent shops. It will here be taken as 2of aninch. Liberal 
allowance should be made in ordering the material for lattice 
bars, as there is always more or less waste. 


1655. In ordering the material for beam hangers, the 
length U of that portion of the hanger bar above the center 
of the pin may be found by the formula 


U=1.57(D+2), (254.) 


in which J is the diameter of the pin, and d@ is the thickness 
of the bar. 


1656. Allthe preceding formulas, except formula 254, 
contain a constant c, which is in each case a quantity de- 
pending upon the methods and conditions of the shop work. 
It is, therefore, evident that this quantity, as used in any 
one of the formulas, will probably not have the same value 
when applied to the practice of different shops. The values 
here given are believed to represent a fair average of good 
practice. 

For convenience in using formulas 245 to 252, inclu- 
sive, the results given by each formula, as applied to the 
various sizes, should be tabulated. In actual practice it is 
essential to have the results arranged in convenient tables, 
so that, for any common size, the required length may be 
read at once from the tabie. In preparing each table, 


1040 . DETAILS, BILLS, AND ESTIMATES. 


however, the value of the constant c should conform to the 
practice of the shop for which the tables are to be used. 


1657. Order Lists.—Two examples of parts of order 
lists are given below. List (/7) is the order list for the mate- 
rial required for the end post, Plate, Title: Highway Bridge: 
Derails le bao eis 

The lower end a of the end post is not planed; conse- 
quently, no allowance of extra length need be made for this 
end in ordering. The upper end / of the end post is planed 
ona bevel. In such cases, the amount given by formula 
244 is usually added to the length of the cover-plate for 
finishing the upper end; it is not, however, always added to 
the length of the channels, although this is done in the 
present case. 

Plates with the corners sheared off, as the tongues of the 
pin plates at the hip joint, are generally listed in rectangu- 
lar form, without reference to the shearing, which is usually 
done at the bridge shops. They are almost always ordered 
as one plate (or more, if necessary) of length equal to the 
aggregate length of the several plates required of the same 
size, and are sheared into the required lengths and forms at 
the bridge shops. For plates sheared to dimensions, the 
mills charge a higher price than for plates simply cut to 
ordinary lengths. 

As rivet iron is always carried in Sage lists of the shop 
rivets required are not commonly given on the order lists, 
although it has been done in the present case. When lists 
of rivets are given, however, all rivets of the same length 
are generally given in the same item. 


1658. List (/) is the order list for the material required 
to form the members and details shown on Plate, Title: 
Highway Bridge: Details IV, Figs. 1 to 12. The ordered 
dimensions are those required to make the finished dimen- 
sions given on the shop lists in Art. 1645. The ordered 
dimensions of the material should be given on the shop lists 
and working drawings, in order that the workmen may be 
able to select easily the proper material for each member. 


DETAILS, BILLS, AND ESTIMATES. 1041 


The ordered lengths of forged bars are seldom expressed 
by fractions smaller than eighths of an inch, although six- 
teenths may sometimes be used. In making out order lists, 
it is well to use, in each case, the eighth of an inch next 


above the calculated length. 


(/7) 


ORDER LIST. 


For 4 End Posts. 


Material, Wrought Tron. 






































W’ cht Length. 
afark: Number| Name of Size. 1b. . To’al| Ord- 
R’quir’d Shape. Inches. pen Rt} Ft. In. Wt. |der’d 
ab 8 |Chans. 8 16 | 25 |1014 O 
ab 4 |Angles. | 24x 24] 4 3 | 42 O 
ao 4 |Plates. 2x ¢ 25 | 1013 O 
ab 8 |Plates. 6 X q5 Leeds O 
ab 8 |Plates. 6 Xq 1 | 13 O 
ab 8 |Plates. x ox) ene O 
ab 180 |Bars. 1¢x 4 1 | 12 S 
Where Used. Shop. Rivets 
Cov. Pl. | 512 |O heads.| $x 24 S 
Bat. Pl. 72 |O heads.| 8 x 2 S 
Lattice. | 184 |O heads.| #8 x 2} S 
tee, 32 |O heads.| 2x14 S 
Pin Pls. 80 |O heads.| #2 xX 2 S 
lei hema SE 48 |O heads.| $x 18 S 
Pin Pls. 16 |C.S.hé’ds| 2x 128 S 
Field. Rivets. 
Hip Cov.| 16 |O heads.| § xX 28 S 
Hip Cov. 4 |O heads.| 8x 14 S 
PortCon.} 32 |O heads.| # xX 1? S 
PortCon.} 16 |O. heads.| $x 1¢ S 

















1659. 


and weights of channels and angles, as well as the sizes of 





Stock Material and Iron Order.—The sizes 


1042 DETAILS, BILLS, AND ESTIMATES. 


plates and flat bars, most commonly used at bridge works, 
are generally carried in stock. 

Round and square bars of one inch dimensions and less, 
and sometimes the common sizes of much larger bars, are 
carried in stock. 

Rivet iron, turnbuckles, standard and recessed nuts, 
spikes, nails, wood screws, washers, several sizes of bolts, 
and all small extras of like nature are always carried in 
stock. 

small bars, such as the small flat bars used in making 
the heads for cotter pins or the half round bars used for 
making the cotters, are carried in stock, and are cut off in 
small pieces as used. such material’ iss teqiired tobe 
listed upon the order list only for the purpose of checking 
off from the stock lst, and, therefore, the lengths need not 
be given with very great accuracy. But the lengths of the 
larger pieces of stock material, which are to be forged or 
cut to certain dimensions, must be given accurately. 


1660. In making out the iron order, all short pieces of 
the same size (width and thickness) are assembled in one or 
more long pieces of the same aggregate length. Short 
pieces of plates and angles, for such purposes as pin plates, 
batten plates, lateral-hitches, etc., are simply sheared off, 
and require no allowance for cutting. But bars for pins 
are usually cut by turning off, which requires about 4 of 
an inch to be allowed foreach cut. (See formula 250.) 

When the order list has been made out, it is compared 
with the stock list, and such sizes as are in stock are 
marked on the order list with a letter S, and are checked 
off from the stock list. The iron order, or list of required 
material not carried in stock, is then made out from the 
order list. This material is checked off from the order list 
by marking either the letter O or the date on which the 
iron order is made out opposite each item that is trans- 
ferred to the iron order. A copy of the iron order, as thus 
made out, is generally sent directly to the rolling mills by 
the business department of the bridge'works; if it is a large 


DETAILS, BILLS, AND ESTIMATES. 


1045 


(7) 


ORDER LIST. 


For forged Members and Pins. Material, Wrought Tron. 


(Except where otherwise marked.) 


















































Contract No. 78. Shop No. 735. Span 90'0". Sheet No. 
um. . Weight.| Tength, | 
Mark. Pe Name. pee one tae cs ates Ordered. 
quired. Foot. | Feet: |Inches. 

yee 8 | Bars. | 2 x 43 25 | 94 O 
ee 8 | Bars. tx ¢ 6 | 54 5 
Ge" 8 | Bars. ix ¢£ 21 | 64 S 
Bob 8 | Bars. Leesa 20 | 43 O 
Beare bars. | 1." O 26 | 72 S 
ewe embars. || 'L 7 O 26 | 114 S 
ab.| 4 |Bars. | 14"0 6 | 2% O 
Wie wbark:. | Lalo 20 | 11 O 
bc, 6 »Bars.. }el«*’O 6 | 24 S 
bc, G j.Bars. jb.” O 20 | 92 S 
figy:| 8 |\Bars. | 14x 14 6 | 114 O 
iefeie a, Velates: |B. x 2 OQ: 8 O 
14 bic hars. f S* —— 84 S 
a 4. | Bars. 24" O 1 | 24 Sst’l O 
Bape bor Bars. 24" O 1*|-0r St’l O 
c 4 (Bars. |\1t" 0 0 |113 O 
ats.) 20.) Bars. 1h O 0} 4 O 
Lats.| 20 | Bars. ax 35 Chae Gas S) 
Lats.| 20 |40’s 3" 0 | 64 S 
Nuts| 16 | Stand. |For1{"0 5 
Nuts| 32 |Ret. (|For2 ’O S 
Nuts} 8 |Rec. |For1}’oO S 
Gc’ 8 | Tbkls. |For 12’0 0 | 9% S 
mo. | A | Tbkls. |For 1}O 0 | 10 S 
bec 6 | Tbkls. |For 120 0 | 92 S 








1044 DETAILS, BILLS, AND ESTIMATES. 


order, several copies are usually made, by blue-printing or 
otherwise, which are sent to various rolling mills, request- 
ing them to quote prices on the order. 
List (A’) is the iron order for the material ordered from 
order lists (/7) and (/). 
K) 


IRON ORDER. 
Contract No. 578. Shop No. 735. Span 90’ 0". Sheet No. 7. 











Weight. Length. 






































Mark. pare Name. Material. Bas ers RaaRat ee 
ab 8 |Chans. |W. Iron| 8 16 | 25)1044 
ab 4 |Angles.|W. Iron} 24x 24) 4 3| 43 
ab 4 |Plates. |W. Iron|12 x # 25 | 1042 
ab l. \Plates: )We droniig= x! 12} 0 
ab 1 |Plates. |W. Iron} 6 x 7 Loves 
leg 1 .)\Plates. -|We Iron) (§ =e 6] 0 
Be}\ 8 |Bars. |W. Iron) 2 x 43 25 | 94 
i. 8 (|Bars. |W. Iron; 14x 14 6|}114 
Bob 8 iBars. (}Wolron) a x4 20 | 43 
ab, 4 |Bars. |W. Iron} 14” 0 6 | 22 
ab, 4 (Bars. |W. Iron} 14” 0 20 | 11 
G 1 |Bars. |W. Iron| 1f£’ 0 10 | 114 
a 1 |Bars. |M. Steel] 22’ 0 17 | 34 











LUMBER BILL. 


1661. General Observations Concerning Tim- 
ber.—Of the bills of material required in the construction 
of a bridge, the last bill to be made out is the bill of the 
lumber. The kind of lumber and the essential dimensions 
of the same to be used for the various purposes are given 
on the stress sheet, from which information the lumber bill 
is made out. | 

As kept in stock by dealers, the lengths of pine lumber 


DETAILS, BILLS, AND ESTIMATES. 1045 


are commonly multiples of two feet, but oak lumber can 
usually be obtained in lengths of odd feet also. When lum- 
ber is ordered in lengths of odd feet and can not be fur- 
nished as ordered, it is furnished in the next longer lengths 
of even feet. Lengths not greater than 20 feet are easily 
obtainable, but greater lengths are difficult to obtain, and 
are expensive. Therefore, the panel lengths of bridges in 
which timber joists or stringers are to be used should, if 
possible, not exceed 20 feet. 

As commonly sawed, timber is nearly always a few inches 
longer than its nominal length. Consequently, if the panel 
lengths of a bridge are in even feet, the joists for the bridge, 
if ordered of a nominal length the same as the length of 
panel, will be long enough to give full bearings upon the 
floor-beams. It is necessary for the joists in the end panels 
of a bridge to reach to the extreme end of the bridge, or 
somewhat beyond the extremities of the shoes; this requires 
the joists in the end panels to be about a foot longer than 
those in the intermediate panels. This will be readily 
understood by reference to Plate, Title: Highway Bridge: 
General Drawing, Fig. 1. 


1662. Relative Heights and Arrangement of 
Joists.—Timbers of the same nominal width always vary 
slightly in their actual widths. Consequently, in order that 
joists may have a uniform height over bearings, they should 
be sized down to uniform widths at the ends. The uniform 
width to which the joists in a bridge are to be sized is 
usually + inch less than their nominal width. 

That portion of a bridge abutment upon which the shoes 
and bed-plates rest is called the bridge seat, and that 
portion which extends above the bridge seat for the purpose 
of a retaining wall is called the back wall. By reference 
to the partial elevation and top view of the abutment shown 
in-Higs. 1 and 2 of the plate just referred to, it will be 
noticed that a step in the masonry, six inches above the 
bridge seat, projects out seven inches from the back wall. 
This is to support the ends of the joists at the expansion 


1046 DETAILS, BILLS, AND ESTIMATES. 


end of the bridge, which is necessary in this case, in order 
that the joists may clear the lateral rod. At the expansion 
shoe, the top of the lateral rodis$ +2+4+24+ 2-4 14 = 5} 
inches above the bridge seat. (See Plate, Title: Highway 
Bridge: Details III, Figs. 5, 7, 8.) 

The top of the roadway floor plank will be 11$-+4 3 = 14} 
inches above this step, or just even with the top of the back 
wall. At the expansion end of the bridge, the center of the 
shoe pin will be $+ 2+ $+ 5 = 82 inches above the bridge 
seat (see same Plate and Figs.), or 83 — 6 = 28 inches above 
the masonry step that is to support the joists. At the inter- 
mediate panel points, or joints, of the lower chord, the tops 
of the floor-beams will be 42 inches below the centers of the 
lower chord pins, or 4% — 22 = 22 inches lower, with respect 
to the lower chord pins, than the top of the masonry step 
that is to support the ends of the joists at the expansion 
end of the bridge. Consequently, in order that the joists 
shall all have the same elevation, with reference to the lower 
chord pins, it will be necessary to place a bearing plank or 
riser piece, about 22 inches thick, upon the top of each floor- 
beam, for the joists to rest upon. Each bearing plank will 
be a 10” & 24” oak plank placed lengthwise upon the top of 
the floor-beam, as shown in Plate, Title: Highway Bridge: 
General Drawing, Fig. 2. 

These planks should be secured to the flange of the floor- 
beam, either by bolts passing through the flange angles or 
by steel nails clinched under them. As the bolt holes 
would cut out a portion of the flange section, the latter ex- 
pedient will here be employed. Such bearing planks are 
not very commonly used; the joists being generally placed 
directly upon the flange of the floor-beam. Itis not really 
essential for all portions of the floor to have the same eleva- 
tion with reference to the lower chord pins, and, there- 
fore, such bearing planks may be omitted without any real 
detriment to the structure. 

At the expansion end of the bridge, it will be necessary 
for a notch to be cut in the lower edge of each joist, in order 
that it may clear the shoe strut. Although this is not a 


DETAILS, BILLS, AND ESTIMATES. 1047 


really commendable thing to do, the notch is so near to the 
end of the joists, that it will probably not weaken them. 
This could be avoided only by raising the joists 314 inches 
higher. 


1663. The Bill of Lumber.—For this bridge, the 
bill of lumber will be as follows (see stress sheet): 


BILL OF LUMBER. 





|S ifs mp ha ea aie | a RR c cn wae saat Gontrade Noe. 
ero atah tn eee feet Roadway............. feet, clear width, 
Poauekilenoths .2 * PCCU ee aa. Sidewalks............. feet, clear width. 
Num- 
ber of Name. Size. Length. NOE Material. 
idcee Feet, B. M. 





30 Joists oe Oe a MO 1,890 |Yellow Pine 
20 Joists 34°12" | 19’ 0’ 1,330 |Yellow Pine 
Plank 3” Thick 18’ 0” 4,968 |Yellow Pine 








12 |W. Guards} 4’x 6’ 16’ 0" 384 |Yellow Pine 
Total Yellow Pine 8,572 
4 | Bear. Plk.| 24’ 10’ 18’ 0" 150 | White Oak 








It will be noticed that in the items for the joists, wheel- 
guards, and bearing planks, all dimensions are given, while 
for the floor planks only the length and thickness are stated. 
The floor planks may be of any width not less than 7 nor 
more than 10 inches (they are usually of different widths), 
but their aggregate width must be equal to the extreme 
length of the bridge, which will be about 92 feet. This 
will be the case if they give the required number of feet 
board measure. 

The wheel-guard timbers may be in any lengths, uniform 
or varying, but their aggregate length must be sufficient to 
extend the entire length of the bridge, upon each side of the 
roadway, with six inches lap at the joints. 

As lumber is sold by the thousand feet (or hundred feet), 


1048- DETAILS, BILLS, AND ESUIMATES: 


board measure, the number of feet board measure in each 
item should be calculated and written opposite the item in 
the column headed Number of Feet, b. M. 

A foot in board measure is one foot square and 1 inch 
thick. 


SHIPPING BILLS. 


1664. Nature of a Shipping Bill.— When the shop 
drawings, shop lists, order lists, iron order, and lumber bill 
have been made for a bridge, the next office work in hand 
is to make outa detailed list of all members, pieces, and 
materials that are to be shipped to the bridge site and used 
in erecting and completing the bridge. Such a list is called 
a shipping bill. All things listed upon the shipping bill 
are weighed out from the shop and shipped to the bridge site. 

The shipping bill gives a list and partial description of all 
finished members, parts of members, and connecting pieces 
shown on the working drawings and described in the shop 
lists, and is made principally from these. A brief descrip- 
tion of each member is given, witha few essential dimensions, 
in order that each member may be readily identified and 
roughly checked. The shipping bill includes also items of 
material not shown on the drawings nor given in the shop 
lists, such as the field rivets, bolts with nuts and washers, 
spikes, nails, lag screws, paint, etc., required to complete 
the structure, as well as the erection bolts, pilot nuts, and 
other things required in its erection. It will be well to 
notice here the requirements for some of these items of 
material. 


1665. Field Riwvets.—The diameters, lengths, and 
number of field rivets required may be obtained from the 
shop drawings; they will correspond to the vacant holes 
shown on the drawings. The number of rivets actually re- 
quired of each size must be increased from ten to fifteen per 
cent. to provide for waste. The percentage of waste depends 
to some extent upon conditions at the bridge site, difficulty 
of erection, etc., and can be estimated only by a very liberal 


DETAILS, BILLS, AND ESTIMATES. 1049 


“approximation. ‘Twelve per cent. is, perhaps, a good aver- 
age allowance for this purpose; it is a convenient practice to 
make the total number of rivets required of each size equal 
to the multiple of ten nearest to, but generally above, the 
estimated number with the percentage added. 


1666. Bolts and Washers.—Ordinary bolts will be 
required to bolt the wheel-guards to the floor planks. Bolts 
# of an inch in diameter should be used for this purpose ; 
each bolt should have two washers. These bolts should, under 
ordinary conditions, be spaced about 6 feet apart along each 
wheel-guard. Hence, the number z of bolts required for the 
wheel-guards in one roadway will be given by the formula 


L 
n= 3 - 2, (255.) 


in which Z is the extreme length of span in feet, which may 

commonly be assumed to be 2 feet longer than the length 

from center to center of end pins. Any fraction in the 
: elas 2 

expression -~ may be neglected. 

In order to afford ample drainage for the roadway, the 
wheel-guards are elevated from 1 to 2 inches above the floor 
planks, by means of shims, which consist of pieces of plank 
about a foot long, placed under the wheel-guard of each 
bolt. The wheel-guard is laid flat, i. e., with its broadest 
dimension horizontal. The bolt passes through the wheel- 
guard, shim, and floor plank. Hence, the length / of the bolt, 
under nead, will be given by the formula 


=Et+e, (256.) 
in which g is the grip of the bolt, equal to the aggregate 
thickness of the wheel-guard, floor plank, and shim, and ¢ is 
a constant which, for bolts not more than } of an inch in 
diameter, may be taken equal to 1 inch. 


EXAMPLE.—(a) What number and (4) what length of bolts will be 
required for the wheel-guards of the bridge shown on the Mechanical 
_ Drawing plates, it being assumed that the wheel-guard is to be 

blocked up by 2-inch shims ? 


1050 DETAILS, BILLS, AND EsTIMATES: 


SoLuTION.—(a) By formula 255, the required number of bolts is 


92 
3 + 2 = 32 bolts. Ans. 


(2) The thicknesses of the wheel-guard, shim, and floor plank are 
4, 2, and 3 inches, respectively. Hence, the length under head of each 
bolt will be 4+2+383-+1=10inches. Ans. 


1667. Spikesand Nails.—Each roadway plank should 
be spiked to each joist upon which it rests by two spikes. 
As the widths of the planks should average about 9 inches, 
the total number of spikes z required for this purpose will 
be given by the formula 

ee 
3 ] 
in which Z is the extreme length of the span, and /V is the 
number of lines of joists. 

Some specifications require the spikes used in spiking the 
roadway planks to the joists to be ;-inch wrought spikes 
7? inches long. But it is doubtful whether such large spikes 
are really required or even advantageous. Common 
60-penny nails (1. e., cut spikes, 6 inches long) are frequently 
used. Steel-wire spikes (round) are very satisfactory for 
this purpose. 

Nails and spikes are always sold and shipped by the 
pound or keg. The number of spikes required for the floor 
planks may be found by applying formula 257, and the 
number of pounds (or kegs) necessary, in order to give the 
required number of spikes, may be obtained from Table 43. 
An allowance of about 10 per cent. should be made for 
waste. 





(257.) 


EXAMPLE.—If steel-wire spikes 6 inches long are used for the floor 
planks of the bridge shown on the Mechanical Drawing plates, (a) how 
many spikes, and (4) how many pounds of spikes will be required ? 


SOLUTION.—(a) As given by formula 257, the number of spikes to 


8x 92 x 10 
— —— = 2,458. If 10 per cent. be added for waste, the 


number of spikes required will be 2,458 + 245 = 2,700. Ans. (6) By 
reference to Table 48, it is found that, for steel-wire spikes 6 inches 
long, there are 10 spikes to the pound. Hence, the number of pounds 


2,700 
’ is Or 
ie = 270 lb. Ans. 


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1052 DETAILS, BILLS, AND ESTIMATES. 


Wrought spikes, sometimes called ship spikes or boat 
spikes, are usually sold by the keg of 150 pounds, and are 
shipped by the keg, except where a smaller amount is re- 
quired. If, in the preceding example, -j;-inch wrought 
spikes 7 inches long were designated, there would be required 
(see Table 43) Jane =4kegsand 52 pounds. . 

A few steel-wire nails will be required to fasten the 
bearing planks upon the tops of the floor-beams. These 
nails will be driven through the planks outside (on each side) 
of the floor-beam flanges, then clinched under the flanges. 
Nails 44 inches long will be suitable for this purpose. The 
number of nails may be estimated at 2 nails per foot of 
beam, making the number of nails to be used equal to 
2x18 x4—144; and, by adding 10 per cent. for waste, the 
number of nails required will be equal to 144-+ 15 = 159. 
If 44-inch steel-wire nails are used, then there will be 


: 9 
required (see Table 43) a8 — 7 pounds, near enough. 


1668. Erection Bolts.—These bolts are used to 
secure, temporarily, the various riveted connections, hold- 
ing the connecting parts in position until the field rivets 
can be driven. It is, therefore, evident that the sizes and 
lengths of the erection bolts may be determined from the 
rivet holes shown vacant on the shop drawings, in much 
the same manner as the sizes and lengths of field rivets; the 
number of erection bolts required may be somewhat less 
than the number of field rivets required. The length of an 
erection bolt, however, being adjustable, need not be 
determined with very great accuracy, but the same length 
of bolt may be used for different grips, varying through a 
range of }inch, or evenmore. The length, under head /, of 
an erection bolt may be given by the formula 


f=g+d++e, (258.) 
in which gis the grip and d is the diameter of the bolt, andc 


is a constant which may have a value of from } to % of an 
inch, 


tay a¥ 
tot) eats WY. 


‘. >} "ey 9)y:! r ij 
1 y etesh") “ha 
55 *er ginlti-1 
1» ened Yee 

a ‘gt opel"t-1 
41) aod Se 
a "sx of i} 


f 
1! 
\" ; 
: 


Bs 


4 ee 


oo 
VY 


= 
—_ 


| ssi 
= 00000 


rete 

bHoadl nooo tl 
etlotl aoitesta 
aip¥ sold 
ey, jot: 


wy th by me aca y 
ee \ 8 
A * 



























































ery Th a i eae “— a. be es ed <a Y, ut “wi - i = p r :, P PT eae + ‘te is ee. oes - 
oe : : SHIPPING BILL. 

PIES ELC yeh [eee eee ee, oa Wi oo ee WG tO. Sore eo ee a Pee CONTACTING. ag z 
cea aes Steere. tect tort, SUNY EIRO NS | MMM Seen i cree RE aE ADEA ARR RD ot TEC «Sk eee aa 
Bene Si Roadway................feet, clear width ib ae oor aad eae in eet Pt ee eat See — 
teseeesseeseonene Sidewalks... feet, clear width SET, SEE CE ae Ginn eeees ae ties Marat Str tas oc on Maas. tS 

| No. and | Shipping 
Mark. aes | mee 2 Material in Member. Size of Length. Weight. 
q ‘ dVLeE er. rete 
) { 2-R| ( 1-Plate 12” * 34" | 2-228" | 25’ 558’ C. te C, | 
soe eiges E SS aah pa Chans. @ 16 Ib. cy 
: ( 2-R| § 1-Plate 12” x Y/" r-225" 17-834" C.-fo E 
ae 4 |Top Chords t2-L | } 2-8" Chans. @ 11 Ib. 5-925" i{ 18’ 0%" C. es 

+) , ( 1-Plate 12" k yy" poe (1S 826" Beto ke 
sas gag Peenords ? 2-8" Chans. (@ 11 Ib. . Se? 

Cee Ae nites OSts 4-3%' X 2” L’s @ 4.4 lb. Latticed 1-228 Gr he, te OS Ra 
BB, 2 [Portal Struts with! 43%" x2" L’s @ 4.8 Ib. Latticed Robot she tek 
Pe 2 |Lateral Struts 2- = x 4" L’s @ 10.8 lb. | ;. 20 0" K. to E, 
Io B. Aeeinee braces 2-3" X 24%" L's @ 4.4 Ib. 4 316. B. to B. 
aa, : Herat rat 1=-Plate xa 4, ernie : 16° 104%" E. to HK. 
2-314 ” 7 " Ss 4. . : : 

- PR § 1-Plate 24" x 34" 1G-) 3. = Enc toe 
FB 4  |Floor-Beams ) 4-4" X 3" L's @ ats: : | ral ; 
fateh 8 |Beam Hangers 14" X14", 1%' S. Ends with Check Nuts 1-233 2 114%’ B. to E. 
V5 i 8 |Hanger Pls. Gare of 2-2" o 4%" ©. to C. 

re 4 |Separators 8" «x 1" 22" oe obs eae Ua tol 
eA 4 |Lower Chords 4-3" X 2144" L’s @ 4.6 lb. Latticed 2-255 | 17’ Ty. C. to C. 

(here 4 |Lower Chords 4-3" X 2" L’s @ 5.8 lb. Latticed 2-255. Py 1133 C. to C. 
CAC 2  |Lower Chd. Bars 2 Bars 414" x 48" Lattieed 2-223 17 1133" C. to C. 
Bre @ a l4e:Bars 2" <4?" | 2-253" 25' 57, Coit: 
BO 8 |Hip Vert. Rods Lea 2-253 1S) 253" Bete- 6B 
aes 8 (Counters h" X KH", 1%" §. Ends I-1 53" 20’ 3;'5" B. toE 

ras 8 jCounters h" KB", 13x" Ende 93" Turnbuckle 1-228" ee ae B. to E 
a b, 4 |!Lateral Rods 1%" 0, 1%’ S. Ends | I-53" 19 84%" B. toE 
a bh, 4 |Lateral Rods 14%" 0, 1%’ S. Ends, 10’ Turnbuckle 1-153" NO ete B. to E 
Pr Cin} 6 |Lateral Rods eee Opal oe Sends 1-153" Ig. 7 Dato E 

f-€5;) 6 |Lateral Rods I Oe 1%" S. Ends, 93/" Turnbuckle 1-138 550 B. toE 
B Ci 4 jLateral Rods tO: 134" S. Ends St. Nuts} 25° 105% EK. to] 
Cie 2 Lateral Rods Le Lye ». nds mid. Nuts 26) 2 E to E 

a 4 |Chord Pins 237'O; 1196. Grip R. Nuts| 1 2/¢" E. tok 
Bd, ey 12 Chere Pins 2356); 934" Grip R. Nuts Uo" E. tok 

G 4 |Chord Pins 13"Q, 9%" Grip R. Nuts o 11%" E to E. 

ce 20 |Lateral Pins ya, 2254 Grins 34" Cotters o 4 E. tok. 

KS 4 |Pin Washers For 1 34" Pin o 44%" E. toE 

vas 4 |Pin Washers For 237” Pin | o 2%" E. to E 

b 8 |Pin Washers Boras 7 ety | Oo 1 4 ; E. toE 

b 8 |Pin Washers For 2 i" Pin | o oO" E. to B 

. ; (Stand. x34" x op" L's | § 2-238" | 

2 |Anchor Shoes iba SA 736" << PTS Prith Lat. con. | ( I-17%" | 
aa ’ Atan. 2°) Gx aes x 54" L's | { 2-255" | 
2 |Roller Shoes Pl. Ci9 wae “Hi X 13 ‘Shoe St. & Lat. con. ( 1-143 | 
2 |Nests Rollers BC), Ate 14" | | 
2 /|Bed-Plates St, seen a Ok 14 : es 
2 |Bent Anch. Pls. hala clas El 4 336 1-1 | 
12. |Anchor Bolts I" OQ X to with Wedges 
20 |Field Kivets 7 OX 214" UT. Fis | 
20 |Field Rivets % OX 234" Rae 
| - 30. |Field Rivets re (lee ee ous 
50 |Field Rivets % eS 17" 28 
150 |Field Rivets %" OX 1% Elaras ce 
32 |Bolts 4% O X_10 a = 270 
Spikes 6" Steel Wire 7 
Nails 414" Steel Wire 
Paint ; 1 
160 |Erection Bolts a (hae. F Ur 
40 |Erection Bolts Uo eb eo ae Che = F 
Pilot Nuts For 2: 4, Pin | 
| Pilot Nuts For 13¢" Pin | 








DETAILS, BILLS, AND ESTIMATES. 1053 


1669. Pilot Nuts.—One pilot nut is required for each 
size of the pin, and it is always well to have extra pilot nuts 
of each size, as they are liable to be lost. 

Erecting boits and pilot nuts are used simply during the 
erection of a bridge. They do not remain in the structure, 
but may be used again in the erection of other structures. 
Erecting foremen usually keep supplied with a limited num- 
ber of pilot nuts and erecting bolts remaining from structures 
previously erected, and carried as a part of their erecting 
outfit. Erection bolts and nuts should, however, be listed 
upon the shipping bill. 


1670. Lumber Bill.—The bill of lumber required for 
the bridge proper is usually ordered of a lumber mill or 
dealer, and by him delivered directly at the bridge site. In 
such cases, it, of course, does not appear upon the shipping 
bill, the latter being a bill of the material shipped from the 
bridge works, _ 

The lumber and other material required for false work in 
the erection of the structure, as well as the outfit of tools 
required, are matters usually left in charge of the erecting 
foremen, and will not be considered here. 


1671. Shipping Bill.—The accompanying complete 
shipping bill is for the bridge shown on the Mechanical 
Drawing plates. In order to show a form of blank sheet 
suitable for the shipping bill, the blanks in the heading of 
the sheet are not filled out. 


THE ERECTION DIAGRAM. 


1672. Asketch or diagram showing the proper posi- 
tions of the various members in a bridge should be made for 
the guidance of the erecting foreman. Sucha sketch is called 
an erection diagram. By the aid of it the erector may 
readily ascertain the correct position of each member and 
piece entering into the construction of the bridge. 

The erection diagram is simply a skeleton diagram of the 
truss and lateral systems, somewhat similar to the stress 


1054 DETAILS, BILLS, AND ESTIMATES. 


sheet, having written along each member a description of 
the material composing its section, with its length, and giv- 
ing also the dimensions of each pin and such other informa- 
tion as may be essential. A partial plan of one lower chord 
is also drawn to an exaggerated scale, showing the arrange- 
ment of the chord bars and the manner in which the chord 
bars, tie bars, counters, and beam hangers are packed upon 
each lower chord pin, with the dimensions and positions of 
the pin washers used. It is often not necessary to show 
more than the mere arrangement of the various members as 
packed upon each pin. If the truss is symmetrical, both 
with reference to the center of its span and the center line 
of its roadway, it will not be necessary for more than one- 
half of one truss, and but little more than a quarter of each 
lateral system, to be shown in the erection diagram. 

Fig. 336 is the erection diagram for the bridge we have 
been considering. It will be readily understood. 


ESTIMATES. 


THE APPROXIMATE, OR PRELIMINARY, ESTI- 
MATES. 


1673. General Methods and Process.—At some 
point during the process of making the design for a bridge, 
and previous to its actual construction, it is necessary to 
make an estimate of the weight of the metal required in its 
construction. An approximate estimate of the weight is 
usually made directly after the completion of the stress 
sheet. This estimate is often called a preliminary esti- 
mate, although in some cases a rough estimate has been 
previously made. If no drawings of the details are made 
before the letting of the contract, the preliminary estimate, 
as made from the stress sheet, forms the basis for the esti- 
mate of cost in submitting the proposal and making the 
contract for the construction of the bridge. In many cases 
the preliminary estimate is the only estimate of weigit 
made. Although not usually a close estimate, yet, when 








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ARG RQ ay 
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aba 4-325 “3s. Lat. bc=4—337 2 2"L's. Leet. rg cc= 2-44" 38" hat. 
a 17-1122" C. to C. b 17-1122" C.to C. C 17-1122" C.toC. 
13” C.Pin. -13"C. Pin 2-13" C.Pin. 
Bs 
ES P ; : 
= we = ey R o 
sax |S % S| SF sas 
F meg = Se. <X 1 CAS 
S a4 } wiles = ma ZX e y 
Wt Se T “a lie ONS 
S~ 2 SY s| dey > eo 
g nS al ES A 
Ss a8 
= a <. cae RRS 
Center Line. 
23’ Pin. 
” 23” Pin. Pr Cate 23" Pin. 
P.W.ig— 9F" Grip. L.C.7%2"P.P. D.C. 7'xF P.P. 54” (oe erate: 
= : IP.dg xe P. PE 
lid "Dp re ” 150 
Pa lagi wo [imi | MT. 242 13 Se Ld. abt 
= wy 
H. Vid xi po a Hi Fila q a C.F. xg 
i gr. 4j x1; Bers i 12" wt 
fT, V.1 y he - Pott bee . 
MDL 2552" sachet $d " 





LOU EPP. 








Contract No. 578. 
aE Des 8 Oi RRB os 
Height of Truss 


Clear Roadway.... 


6 SPQ e) & st 





PW. 








L.0.7x2'P.P. 1.0.72" PP. 
8”CSeparator. 
On Hanger. 
FIG. 336. 

Erection Diagram. 
Location, Jones’ Crossing, Sycamore County, Pa. 
et), JEhe st BLOF SANK... 5 lore 38" Vellow Pine. 
= 18 feet. fotsts, 10 lines, 84" x 12" Spee Pine. 
= 18 feet. Wheel-Guard, 2 lines 4" Yellow Pine. 


DETAILS, BILLS, AND ESTIMATES. 1055 


made by an experienced bridge engineer, a preliminary 
estimate will often approximate quite near to the actual 
weight of the structure. If the detail drawings of the 
structure have been made previous to the making of the 
estimate, the latter will, of course, be much closer. 

The preliminary estimate usually gives the same informa- 
tion that is given upon the stress sheet, together with an 
approximate detailed estimate of the weight of the material. 
In fact, in many cases, after the stresses have been deter- 
mined, they are copied upon the estimate sheet, the material 
is proportioned and also written upon it, and the estimate 
is made before making the stress sheet. The stress sheet 
is then made from the estimate sheet, to be submitted with 
the proposal or to form a part of the contract; the esti- 
mate sheet is filed for office reference. 


1674. In making the preliminary estimate, the weight 
per foot of each member is estimated according to the 
material shown on the stress (or estimate) sheet, and this 
weight multiplied by the length of the member, in feet, for 
the total weight of the member. The length of each mem- 
ber, always expressed in feet and decimals of a foot, is taken 
from, center to center of the intersecting members. An 
additional amount is commonly added to the center-to-center 
length of each member, to allow for the weight of certain 
details. This is the common method of providing for the 
weight of, eye-bar heads, loops, upset screw ends, and turn- 
buckles, in estimating the weight of forged tension members. 
For riveted members, the additional weight of the details is 
approximately estimated. Some engineers, however, add 
certain percentages of the estimated weight of the main 
members, to provide for the weight of all details. 


1675. Assumed Lengths and Equivalents.—lIt is 
not possible to give a system of rules for approximate esti- 
mates that will be found satisfactory in all cases. The 
estimator must necessarily be guided by his judgment and 
experience. The following general rules are, perhaps, as 
nearly satisfactory for ready approximations as any that can 








1056 DETAILS, BILLS, AND ESTIMATES. 


be proposed. These rules give a length for each member, 
the weight of which, estimated according to the material of 
its regular section as shown on the stress sheet, is assumed 
to be approximately equivalent to the weight of the member, 
including certain details: . 

The length L of certain members hereafter designated, 
which is to be used in estimating their weight, may be taken 
as given by the formula 


Lata G, (259.) 


in which 7 is the length of the member from center to 
center of the connecting members, and ¢ is a constant which, 
for the various members, may generally have the following 
average values: 


Te. sor each 7end- post] 2.2 ee c= 14 feet 
2, For each end panel of top chordie. Ca le ereet 
3. For each intermediate panel of topchord..c= 4 foot 
A. For each intermediate post)... .e ee Gai) We reCEG 
5. For each riveted tension membetey eee Ce eee 
6. For eachtlateral strut... eee eee Comat) ame oe 
> For each forged eyé-bat ... see eee 6 = ostiies 


the width of the bar. 
8. Foreach adjustable bar having two screw 


ends with nuts... . 2.53). eee G == eect 

9. For each bar having two loop ends...... 0 Lees. 
10. For each adjustable bar having two loop 

ends ‘and'a turnbuckle. )ae see C=) De eeL 


In each of the first three items, the weight of the addi- 
tional length ¢ will be approximately equal to the weight of 
the pzx plates, while in the fourth and fifth items, it will be 
approximately equal to the weight of the pin plates and 
other connecting plates. In the sixth item, the weight of the 
additional length ¢ will be approximately equal to the con- 
nections for the lateral strut. In each of the remaining 
items, the weight of the additional length c will be approxi- 
mately equal to the weight of all details of the members; 
that is, to the amount which the weight of the finished 


_ 


tes ee ee 


DETAILS, BILLS, AND ESTIMATES. 1057 


member exceeds the weight of the plain bar having a 
length /. 

It must be remembered that these values of c, though fair 
average values, are but roughly approximate and may be 
modified according to the conditions of each special case. 


1676. Latticing.—For each single system of latticing 
in which the lattice bars make an angle of about 60 degrees 
with the axis of the member, the aggregate length of the 
lattice bars will be approximately equal to twice the 
center-to-center length of the member. 

For each single system of latticing in which the lattice 
bars make an angle of about 45 degrees with the axis of the 
membez, the aggregate length of the lattice bars will be 
approximately equa? to 1.4 times the center-to-center length 
of the member. 

These lengths are independent of the wzdth of the mem- 
ber. If a double system of latticing is used, or if the mem- 
ber is latticed on both sides with a single system, the 
aggregate length of lattice, as obtained by the above rules, 
should be doubled. 


1677. The lengths of the batten plates are governed by 
the requirements of the specifications. If Cooper’s specifi- 
cations are used, the length of each batten plate will be one 
and one-half times the width of the member, or the aggregate 
length of the batten plate upon each end post or chord 
member, having a cover-plate, will be three times the width 
of the cover-plate. 


1678. Each knee brace may be assumed to be 5 feet 
long. 

1679. The weight of each lateral hitch composed of 
short pieces of angles, similar to that shown in Plate, Title: 
Highway Bridge: Details I, Fig. 4, may be taken equal to 
the weight of 24 feet of the lateral rod connecting upon it. 


1680. Jf the diameters of the chord pins have not been 
determined, in making the estimate, the diameter of all lower 
chord pins and of the hip pin may be assumed equal to about 


1058 DETAILS, BILLS, AND ESTIMATES. 


three-quarters the width of the widest eye-bar in the lower 
chord; the diameter of the remaining pins in the upper 
chord may be assumed to be two-thirds as great as or equal 
to one-half the width of the widest chord bar. 


1681. The lengths of all chord pins may be assumed 
equal to 14 times the width of the cover-plate on the upper 
chord or end post, making no allowance for the reduced 
diameters of the screw ends. The weight of the pins thus 
estimated may be considered to include the weight of the 
nuts and washers. 


1682. J/fa portal ts latticed with ordinary 2” x }" bars, 
the weight of the /a/ticing (including weight of rivet heads), 
in pounds per lineal foot of portal, may be taken equal to 
five times the depth of the portal in feet. 

The aggregate weight of both portal brackets and the 
portal connections for each portal may be taken equal to the 
total weight of 8 feet in length of the portal proper; conse- 
quently, the length of portal having parallel flanges may 
be assumed to be equal to the clear width of roadway plus 
8 feet. 


1683. The weight of all rivet heads in each line of 


rivets in a member may be assumed as follows: 


For 4-inch rivets, +4 pound per lineal foot of member. 
For 3-inch rivets, ? pound per lineal foot of member. 
For #-inch rivets, 8, pound per lineal foot of member. 
For §-inch rivets, 14 pounds per lineal foot of member. 


Ot b 


With this assumption, the two lines of rivets connecting 
a system of latticing may generally be considered as a single 
line of rivets. 


1684. Ji estimating the weight of the floor-beams in a 
bridge having a single roadway and no sidewalks, the length 
of flanges, web-plate, and rivet lines in the flanges may be 
assumed to be equal to 1} times the clear width of roadway 
plus the width of both chords. This will provide for the 
approximate weight of the stiffeners, fillers, and other 
details. 


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Sammie ten nasa nen ee we enna sce eecenanesecesenssa. 














Oar lb. per lin. ft., trusses 
Len th ae : . > ; age ee ee ee BP ‘ 
Emenee 2 eee ft. eo a Load SE TREE oo ID=peéer Jin: ft, trusses, 
ether Roadway eee eclear width Panel Live Load, one truss, Bee ea) ee i 
on nena Sidewalks erees Pemciear width Panel Dead Toe ON Geitige® suey awe es. tae eth: 
aterial, gee der 2 Length of Digeonal iS Maren eee Dea oe eas a 
Se rcCallOie tars, ce eee S 
Member. Stress. ipti ‘ale i i 
Description of Material. Area Given. SUN ARS oe : Weight, 
End Post Pees ter) i2i x 34" 
ab + 19,600 is Chans. @ 16 |b. 4s ee 54 2,538 
attice, 13/" x yi" 
Batten Piet no? x yu’ x 18" ae vee ae ane 
: 56" Rivet Heads ye I : 
Top Chord iat Tesb 32 oe fi . Be a aS 
BRP + 20, 800 ea Chauns. @ to lb. § ae ae 57 ai 2° 
attice: Bars; 1 3/"x 14" : 
Batten. Pis.. abe wi 18” a wee ae ah 
5g" Rivet Heads 67 162 108 ; 
Int. Post + 9,700 | 4-314" & 2" L’s @ 4.4 Ib. 5.28 17.6 4o 70 
Ce + 2,300 | | Lattice, 13/" x Y" -44 1.46 72 aes 
Batten Pls. Se oe I. 75 5.83 oats 20 
56" Rivet Heads 67 30. 24 
Low. Chd — 32,400) | 4-3" KX 24%" L’s @ 4. 6 1b. N.S. Sos 18.4 46 846 
ab — 13,900 | | Lattice Bars, ry x Yr" 44 1.46 2 105 
Batten: Pls.; 6! Kaye 1.5 5. 3 15 
55" Re ey Heads | .67 36 24 
- — 32,400 } | 4-34 “L's @ 5.8 1b. N.S. saay | 23:2 46 1,067 
— 13,900 § roe” ee ly Ay 4A 1.46 72 “Tos 
Batten Pls., 6" oe ae 1.5 | 5. B 15 
cates et Heads .67 56 22 
' == A600 11) Beabbars 412" < 18", N.S. = 6, 150 (Pe eee 20. 
a¢ — 20,800 § Lattice ioe 13" x y" of oie ee a : ee 
5%" Rivet Heads 67 18 12 
H. Vert. — 16,200 } B 
Bob — 4,600 § 2-Bars, 1° X 1" 2.0 6.67 41 293 
Ties ee Du] SOO) ” it 
Be ti, ess pele sey Sots 3.25 10.83 53-7 582 
Cc — 13,750 |2-Bars, 7%" X 7%" 1.53 5.1 62 316 
Pins 8-3" OC x 15” long (steel) 24.00 ine) 240 
-2" OG X 15” long 10.45 2.5 6 
6-Lateral Hitches for 1" QO 2.61 13 39 
Total Weight of one Truss, 10,014 
‘Total Weight of two Trusses, 20,028 
ee OE — 3,700 |4-Rods, 1" QO 79 2.61 112.8 204 
E& eRods,.2” 'O -79 2.61 56.4 147 
ab, —14,900 | 4-Rods, 1%"O 99 3-31 126.8 420 
bc, — 8,200 |4-Rods, 1° QO 279 2.6% 126.8 331 
OG, — 2,200 |2-Rods, 1" O 79 2:61 63.4 165 
BB; 4= 314" X24" L’s @ 4.8 lb "6 IQ.2 } 
Latticed 2 feet deep 10. Ph ee mate 
CE 2-5" 4" L’s @ 10.8 lb. 6.48 21.6 4o 864 
KB a es 24" oe @ 4.4 lb. 8.8 20 17 
aa P16 xX ' J a | 
1 2-434" X 24! Vie @ 4.8 Ib: 4.38 | 14.6 20 292 
4-Fl. Bms. | — 53,700 Web Pl., 24" K 3%" X 20-0" 9.0 30. 92 2,760 
4-4" X 3" L’s @ 8.4 lb., 26-0" 33.6 92 3,091 
5%" Rivet Heads 133 g2 | 127 
8—-Hangers + Ges 1.56 ata 96 a 
: Sioce Eilers, and Bed PI. | 310 
Bolts, Spikes, and Nails 32 
Total Weight of Metal, | 31,842 



























































DETAILS, BILLS, AND ESTIMATES. 1059 


1685. ln estimating the weight of the forged beaim 
hangers, the length of the rod forming each hanger may be 
assumed to be equal to twice the nominal depth of the floor- 
beam plus 8 feet. This will include the approximate weight 
of upset ends, nuts, and hanger plate. 


1686. Lhe total weight W of the shoes, bed-plates, rollers, 
and anchor bolts for one span may be roughly approximated 
by the formula 

PaO (260.) 


in which S is the span, 4 is the clear width of the roadway, 
and cis a variable coefficient which may be taken equal to 
a8 with a minimum value of $. 

1687. Zhe total weight of bolts, spikes, and natls re- 
quired for the roadway floor may also be roughly estimated 
by formula 260 by giving ¢ a value of .2. 

In estimating the weights of structures, the tables of the 
weights per foot of the various sizes of round, square, and 
rectangular sections, given in structural hand-books, will be 
found very convenient, if not indispensable. The sectional 
areas of most of the members are given on both the stress 
sheet and the estimate sheet, and, for such members, the 
weights per foot may be most quickly obtained from the 
sectional areas. This can not be done, however, in the case 
of riveted tension members for which the net section only is 
given. 


1688. The Estimate of Weight.—The approximate 
estimate of the weight of the metal in the bridge is given on 
the accompanying sheet. This estimate is made wholly from 
the informaticn given upon the stress sheet shown in Fig. 
306, Art. 1452. In this estimate, the weights per foot of 
rectangular bars, and of those members for which the gross 
sectional areas are given, are obtained from the areas. The 
weights of round bars are obtained by formula 153, Art. 
1487. This formula applies to steel, and, therefore, the 
results must be reduced 2 per cent. for iron. The lengths 


1060 DETAILS, BILLS; AND ESTIMATES. 


of all members, as used in this estimate, are the lengths ob- 
tained by the preceding formulas for assumed equivalents. 


1689. Accuracy of the Dead Load.—When the 
estimate of the weight of the metal in the structure has been 
made, the designer can readily ascertain whether the proper 
amount of dead load was assumed for the structure in cal- 
culating the stresses. In the present~case, the total esti- 
mated weight of the metal work is 31,842, or, practically, 
31,800 pounds. Hence, the weight of the metal work fer 
lineal foot of the bridge is aha = 354 pounds. 

As estimated by formula 9O, Art. 1298, the weight per 
lineal foot of the structure, exclusive of the floor, was found 
to be 352 pounds. ‘This is only 2 pounds per lineal foot in 
excess of the weight as estimated, and the assumed dead 
load may, therefore, be considered correct. 

It will be well to notice, however, that had the unneces- 
sary latticing been omitted from the center panel of the 
lower chord, and the remaining panels of the lower chord 
been formed of eye-bars latticed similar to the center panel, 
instead of being made up with angles, the weight of the 
structure would have been somewhat less. 


THE CLOSE ESTIMATE. 


1690. In some cases the detail drawings for a bridge 
are made before the contract is let for its construction. If 
the structure is designed by a consulting engineer, complete 
drawings are usually made showing all details clearly. In 
such cases it is possible to make a very close preliminary 
estimate of the weight of the structure by calculating the 
weight of each separate piece and estimating the weight of 
the rivet heads. 

The weights per hundred of the rivet heads, as ordinarily 
formed upon rivets of the four sizes most commonly used, 
are as follows: 


DETAILS, BILLS, AND ESTIMATES. 1061 


in. 
2.2 


7a 


Pepreeelerray TIUCISS 6oc.. 0.0. es ellie a ats TTL oe 
Weight tn pounds per 100 heads. .5.% 10.9 thes 2 


Countersunk and flattened heads are commonly counted 
the same as full heads, though countersunk heads should 
really not be counted. 

The length of a lattice bar having two semicircular ends, 
each connected by a single rivet, may be taken equal to the 
length from center to center of rivets plus the width of the 
bar. 

Where the length of a piece is expressed in feet and inches, 
in estimating the weight it will be found convenient to 
reduce the inches to decimals of a foot. 

Results are always taken to the nearest pounds; fractions 
of pounds are not used in the results or total weights. 


1691. Asan example of a portion of a close estimate, 
the weight of the end post, estimated from the shop draw- 
ing, Fig. 1 of Plate Title: Highway Bridge: Details I, is 
given below: 

Weight Total 





No. Material. Size. Length. per Hat Weleht 

1 Cover Plate, 12” x 3" 25' 108" 15.0 388 

2 8” Channels, @ 16lb. 25’ 103’ 32.0 828 

1 24” 24” Angle, @ 4b. 3’ 4B” 4.0 14 

2 Pin Plates, 6" x +5" Ll’ 24" 7.5 21 

2 Pin Plates, 6" x 7a" EDO a iad 7.5 20 

2 Batten Plates, 12’x }" ise Aig 20.0 30 
45 Lattice Bars, 13”x +" 1 Fees Fe 1.46 (el 
560 Rivet Heads, For 2” Rivets 10.9 61 
ERE ke ae Ee ee eee 1,433 


In the approximate estimate given in Art. 1688, the 
aggregate weight of two end posts was found to be 2,538 +- 
2, 849 
PA PAE 8 Is, or — = 1,425 pounds for 
149 + 60-+ 10 ,849 pounds, o1 9 p 
each end post. This differs by only 8 pounds from the 
above close estimate. 


Where ends are beveled, or corners are cut off, it is, in 





1062 DETAILS, BILLS, AND ESTIMATES. 


most cases, customary to estimate them as though full and 
square, making no deduction for the metal cut away. ‘This 
is because the material cut away is simply wasted and must 
be paid for the same as any other portion of the bill of 
material. For the same reason, no deduction is made for 
pin holes and vacant rivet holes. Indeed, for the same 
general reason, it is customary in some bridge offices to 
estimate the weight of the vzve/s required, instead of the 
rivet heads, as it is desired to arrive at the weight of 
material required to manufacture the structure, rather than 
the weight of the finished structure. In other bridge 
offices, however, it is customary to estimate the weight of 
the finished* members. — The: latter] practices ie= newmlost 
common, and, with the exceptions noticed above, is followed 
here. 

In this connection, it will be well to remark that, in roll- 
ing the material, the rolling mills usually demand to be 
allowed a variation in weight of 24 per cent. from the 
specified weight. It is thus evident that it is useless to 
attempt to be exceedingly exact in making estimates of 
weight. Beyond a reasonable degree of accuracy, any 
effort in the direction of exact estimates is time wasted. 


METAL JOISTS AND STRINGERS. 


1692. Description.—Thus far in the study of bridge 
designing, wood joists are the only ones that have been 
noticed. Metal joists, however, are often used for bridges, 
especially in cities and where the traffic is heavy. They 
are generally solid rolled beams having a cross-section of a 
form somewhat similar to the letter I; such beams are 
known as I-beams (sometimes written eye-beams). I-beam 
joists usually rest upon the upper flanges of the floor- 
beams, though they are sometimes supported upon angle 
lugs riveted to the web of the floor-beam; they are riveted 
to the flanges, or to the lugs, as the case may be. The 
floor is laid directly upon the I-beams; if a plank floor, it is 


DETAILS, BILLS, AND ESTIMATES: 1063 


usually fastened by steel-wire spikes driven each side of the 
joists and clinched under the flanges. 


1693. Strength of I-Beams.—The various proper- 
ties of I-beams of the different sizes rolled, together with 
convenient tables of the safe uniform loads for the same, 
will be found in any structural hand-book. From the 
tables of safe loads, the size of I-beams required for any 
ordinary load and span (panel length) can be selected at 
once, without calculation. 

For concéitrated or unusual loading, it is necessary to 
find the bending moment upon the I-beam. The student 
has learned how to find the bending moment upon a sim- 
ple beam under any system of loads. Having obtained the 
bending moment, in inch pounds, it is only necessary to 
select, from a table of the properties of I-beams, the size of 
beam which will give a resisting moment equal to the bend- 
ing moment found. 

The moment of resistance 7 of a solid beam is (formula 
23, Art. 1243) e 7 


& 


i 


In the case of steel or wrought-iron I-beams having equal 
flanges, c is equal to one-half the depth of the beam. As 
the moment of resistance X must in all cases be equal to the 
bending moment ./, the value of the latter quantity, in inch- 
pounds, should be used for X. 

By dividing the moment of resistance, as expressed by the 
above formula, by S, the numerical values of the resulting 
quotient may be readily tabulated for different sizes of 


I-beams. The quotient which will be designated here by 


Q, has been called the section modulus. This appears to 
be an appropriate name, and will here be used. The value 
of QO may be readily obtained by dividing both terms of the 
preceding equation by S, as follows : 


Q===+. (261.) 


1064. DETAILS, BILLS, AND ESTIMATES: 






























































| Radius of Gyration, Neu- 
tral Axis as before. 


| 


Se = = = F&F SS FS FS fF 


~ 


~ 


Cave GS IN 203) G5 
WP oi ONS eS 


N 
12) 


.08 
.20 


.O4 
i 


Io 


0.99 


0.95 
0.91 


0.87 


On/7 
0. 66 


0.59 


1694. The following table gives various properties of 
the steel I-beams rolled by the Carnegie Steel Company, 
Limited : 

TABLE 44. 
PROPERTIES OF STEEL I-BEAMS. 
32 22 |2 |e. |82 
Bo Sohal ee ee ae 
oa A a ag |d oo 
- Cus a i) a pepe 
e 2 SoS Ae eS er hate hoc ee 

di |B ly #1 Bae Moless lis sess cele neaee 

gobs | ee) ig se eee ee alee 

role Us os ee arte el Sa soma e RY. by re el SS 
is Mier ean on am OC O| 90a se: [ha | OG ei 

Ope | wl g Og oe teen ree emerge a |eado 

rea ° by |t.6.8 loo oat eo Mees O_We 

a] | 8 | Se log \ES eee ea ee ae 

2 - 3 a = ae 5) Sr oe Sa Be 
hohe RI Dia forapibanl febrile: arise ae Q r Y be 
24 | 80 | 23.5 |-50}| 6.95 |.0123] 2059.31171.6/ 9.42 | 41.6 
20 | 80 | 23.5 |.00| 7.00 |.015 | 1449.2/144- 0l7c85 45. 
2O G4 | TS. One oo Bone 1146.0/114.6] 7.80 | 27.3 
Ts} 80} 23.5 1.9797 | 6.47 1.020 1a OS OO Asien: sate 
Von) God iO a Oot 644.0} 85.9] 6.04 | 30.4 
15 | 50.14.93 eA SW 5-75 42020 heb eto OlOroO sean 
CS |oAd ei LecOn 4 Osan oS 424.1] 56.6] 5.94 | 14.0 
[2 |°40 ,TIj71%39 | 5. 50)/:025 | 251. eA G led oo wet one 
L2Q 22 EO aes S eee S 222531 2770) (A Oba alone 
TO} BIN 0.7.1 +37.) 5-001, 029. hb Okrs| asa. anArOoman 
TO:4635,7| Fo 5a a ee 4 122-551) 24654. OOl nes 

O7 | 2r-| Cee ee es Onions O4 ALLOW PTO mss ea 

8 | 18) 5.3]-25] 4-25 |-037 | 57-8] 14.4] 3.30 | 4.35 

a) Ae CA a ee oe ee 38.0110.86| 2.92 | 3.42 

6] 1324 2.3452 2eeeoreOn Gg 23/5 Toca. Venmen2 7 

5. | FOR: 23 309a 2 2egeoareanG 12.4) 4.00) 27050-1220 

4 TA <2, Tob siemens, Cale yas 5. tie2 ont. OG) hong 

3 6) _ 1:0 16¢20)) @-20uo0. 2.0) TET Al Te 2 t MiG eee 














Cunt 





The properties of I-beams given in this table are for the 


DETAILS, BILLS, AND ESTIMATES. 1065 


minimum weight to which each pattern can be rolled. It 
will be noticed that, in several cases, more than one pattern 
is used for the same depth of beam. 

From formula 261 it isevident that, having obtained the 
bending moment J/ in inch-pounds, it is only necessary to 
divide it by the allowed unit stress, and select from the 
table a size of I-beam having a value of QG equal to the 
quotient. 


M 
In case the value of aS does not correspond to any value 
of QO given in the table, but is intermediate between any 
two values of Q there given for the same depth of beam, 
the zext lower value of QO should be selected from the table 


and subtracted from = calling the remainder Q,. This is 


expressed by the formula 


eee (262.) 


BEA! ae a a 





Then, the additional weight per foot JV, necessary to 
M ; 
give the required value of Q (equal to =) will be given 


by the formula 
Q, 
emanate 9.) 


in which @ is the depth of the beam, and JI’, is the required 
additional weight per foot above the tabulated weight. 
That is, W, is the weight per foot necessary to give a section 
From formula 261, 0+ U,= = 
If W, be added to the tabular weight per foot for which the 
value of Q was taken, the sum will be the weight per foot of 
the I-beam giving’ the required moment of resistance. it 
will sometimes be found, however, that the weight per foot 
as thus obtained will be greater than the minimum weight 
of the next larger size of I-beam. In such cases it will 
be more economical to use the larger size of the beam, 


modulus equal to Q.. 


~~) 


1066 DETAILS, BILLS, AND ESTIMATES. 


although it will give a value of Q, and, consequently, 


—_ 


a moment of resistance somewhat in excess of that re- 
quired. Table 44 and formula 263 apply to steel I-beams 
only. 

For iron I-beams, 


OQ 


Veg OR’ (264.) 


But iron I-beams are little used at present. 


EXAMPLE.—What will, according to Cooper’s specifications, be the 
size and weight per foot of an I-beam composed of medium steel, 
required to resist a bending moment of 32,540 foot-pounds ? 


SoLuTIoN.—According to item (@) of the specifications (Art. 1399), 
the unit stress allowed on a solid wrought-iron rolled beam is 12,000 
pounds per square inch, and, according to Art. 1455, medium steel 
may be used for rolled beams with an allowance of 20 per cent. increase 
above the unit stress allowed on wrought iron. Hence, in the present 
case, the allowed unit stress will be 12,000 + .20 x 12,000 = 14,400 
pounds, requiring a value of Q equal to ee == 26.95. ee By 
reference to column Q of Table 44, it will be found that the nearest 
value of Q below this required value is 24.5, which is the section 
modulus of a 10” I-beam weighing 25 pounds per foot. By formula 
262, QO: = 26.95 — 24.5 = 2.45, and by formula 263, W, = tk. = 
5 pounds. Hence, a moment of the resistance of 32,340 foot-pounds 
will be given by a 10” I-beam weighing 25+ 5= 30 pounds per foot. 
Ans, 





POSITIONS AND CONNECTIONS OF FLOOR- 
BEAMS. 


1695. Ina through bridge, the floor-beams are some- 
times supported just below the lower chord, and sometimes 
just above it. These two positions of floor-beams with ref- 
erence to the chord are commonly designated as beams 
below chord and beams above chord, respectively. 


1696. Beams Below Chords, Single Forged 
Hangers.—In the bridge we have been designing, the floor- 
beams are supported below the chord by a single forged 


DETAILS, BILLS, AND ESTIMATES. 1067 


beam hanger or stirrup at each lower chord joint. This 
method of supporting floor-beams has been very extensively 
employed, though it is not now as much used as formerly. 
One of its disadvantages is that when the diagonal members 
of the lower lateral system are attached to the floor-beams, 
which act as lateral struts, effective connections are not 
afforded between the lateral diagonals and the lower chords, 
which also act as the chords of the lateral system. This is 
especially the case when the lateral rods are attached to the 
webs of the floor-beam, as is sometimes done. 


1697. Double Forged Hangers.—In order to de- 
crease the bending moments upon the pins, two hangers at 
each support, called double beam hangers, are some- 
times used. As these can usually be placed adjacent to the 
ties which support the pin, they will evidently produce less 
bending moment upon the pin than a single hanger at the 
center. If floor-beams were absolutely rigid, double beam 
hangers could be employed to advantage. But the material 
in floor-beams possesses elasticity, and, as a beam deflects 
under its load, it throws the greater part of the load upon 
the inner hanger, and, consequently, upon the inner tie bar. 
Certain devices may be used to equalize the load upon the 
hangers, but the cost of such devices will counterbalance 
the saving effected by the use of double hangers, and it will 
probably always be found more advantageous to use single 
hangers. No better connections between the lateral diago- 
nals and the chords are afforded by double hangers than by 
single hangers. 

A disadvantage common to all forged hangers is that, as 
they have screw ends, the nuts are liable to work loose. 
This tendency, however, may be somewhat obviated by the 
use of check nuts, or some one of the various devices known 
as nut-locks, nearly all of which are more or less effective. 
The best forms of beam hangers, however, have no screw 
eas: 


1698. Plate Hangers.—An excellent form of beam 
hanger is composed of one or more plates attached to the end 


IT. [I.—29 


1068 DETAILS, BILLS, AND ESTIMATES. 


of the floor-beam, as shown in Fig. 337. The plate forming 
the hanger is riveted to con- 
necting angles, which also 
serve as end stiffeners for 
the floor-beam. The hanger 
should preferably consist of 
a single plate. It must be 
thick enough to give suff- 
cient bearing upon the pin, 
and, in compliance with for- 
mula 196 of Art. 1598, 
should never be less than 2 
of an inch thick. In some 
cases, in order to avoid an 

FIG. 337. excessive thickness of plate, 
it will be found expedient to attach a shorter reinforcing 
plate to the upper portion of the hangers, as shown. In 
order to prevent bending moment on the rivets attaching 
the connecting angles to the web of the floor-beam, and in 
order better to distribute the stresses upon the latter, the 
filler plates under the connecting angles should be attached 
to the web-plate by one or two rows of rivets besides those 
in the connecting angles. 

In designing the hanger, it is necessary to provide suffi- 
cient bearing surface upon the pin, sufficient metal above 
the pin, and sufficient sectional area on each side of the pin 
hole to resist the tensile stress in compliance with item (/) 
of the specifications (Art. 1399); enough rivets must also 
be used to connect the hanger to the connecting angles and 
to connect the latter to the web. The student has learned 
to do this, and it will not be necessary to give an example. 

The length of the floor-beam, from out to out of connect- 
ing angles, will be equal to the distance from center to 
center of chords minus the thickness of one beam hanger. 
The length of the flange angles and web-plate should be 
about $ of an inch less than this. The plate hanger is, in 
some respects, the best beam hanger yet devised. It does 
not, however, form any better connection between the 








DETAILS, BILLS, AND ESTIMATES. 1069 


lateral diagonals and the chords than the forged hanger, 
when the lateral diagonals are connected to the floor beam. 


1699. Stiff Beam Hangers.—Floor-beams of Pratt 
trusses are sometimes supported below the chord by rivet- 
ing them to the angles, channels, or other shapes forming 
the vertical members, which are extended below the chords 
for this purpose. This forms an excellent attachment for 
the floor-beams, and affords efficient connections for the 
lateral diagonals, but it is not economical, and, for this 
reason, not much used in highway bridges. 

The objection noticed with regard to double hangers, 
namely, that when the beam deflects under its load the 
inner bearings will take the greater part of the load, to 
some extent applies to this form of support also. This con- 
dition is, however, somewhat counteracted by the stiffness 
of the posts, and may be further obviated by the use of deep 
(and, consequently, stiff) floor-beams. In designing this 
form of support, the bearing upon the pins and attachment 
of pin plates must be sufficient to provide for both the stress 
upon the post and the load upon the beam. 


1700. Beams Above Chords.—In through Pratt 
truss bridges, the floor-beams are not uncommonly sup- 
ported above the lower chords. Where the head-room is 
sufficient to allow it, this is the best position for the floor- 
beam; it affords excellent connective details and is econom- 
ical. With this detail, the lateral rods may be attached to 
the lower flanges of the floor-beams; in which case, stress in 
the lateral rods will neutralize a small amount of the tension 
in these flanges. 

The floor-beams are simply riveted to the vertical mem- 
bers, the form of the connection depending upon the form 
of the member. If each of the posts consists of four angles, 
latticed in the form shown in Plate, Title: Highway Bridge: 
Details I, Fig. 3, the floor-beam is usually riveted between 
the angles forming the post, as shown in Fig. 338. In this 
detail the pin plates must be proportioned to take not 
only the stress upon the post, but also one-half the total load 


1070. DETAILS; BILLS, AND Hs TIMATES: 


upon the beam. In order that the beam may be placed 
near the lower ends of the angles forming the post, the 
metal along the center line of the 
inner pin plate must be cut away 
through the upper portion of the 
plate, in order to straddle the web- 
plate of the beam. The metal is cut 
away by punching a row of contiguous 
holes with a square punch, making a 
continuous cut for the proper distance 
down the center of the plate, begin- 
ning attheupperend. ‘There is some 
objection to thus cutting a slot down 
the center of the inner pin plate, but 
if it is not done it will be necessary 
to elevate the beam sufficiently to 
clear the tops of the pin plates, which 
FIc. 338. would further decrease the head-room 
and also require a stay plate in the post below the floor-beam. 
The condition of unequal loading upon the pin plates due 
to the deflection of the beam, noticed with regard to double 
hangers and the attachment to the post below the chord, 
will, to some extent, be present in this detail also, and will 
have the further disadvantage of producing a bending 
moment upon the post. To obviate this, floor-beams are 
sometimes made to connect upon a pin placed in the axis of 
the post. Various other devices are used to deliver the 
floor-beam load equally upon the pin plates. But, if the 
floor-beam is made deep enough to prevent excessive deflec- 
tion, the simple detail shown in Fig. 338 is believed to be 
about as efficient as any that can be devised. It is to be 
noticed that the deflection produced in the post is usually in 
the plane of its greatest strength, and that, while slight 
deflection is produced in the post, it is by the beam also 
supported against further deflection. 
The detail represented in Fig. 338 is for connecting the 
floor-beam shown in Plate, Title: Highway Bridge: Details 
II, Fig. 4, to the post shown in Plate I, same title, Fig. 3. 








DETAILS, BILLS, AND ESTIMATES. 1071 


NAME PLATES AND RAILINGS. 


1ZO1. These two features of the design of bridges have 
thus far been entirely neglected. The design of either the 
name plates or the railing does not involve any real prin- 
ciples of engineering, and will, therefore, require but a 
passing notice. 

Name Plates.—Upon nearly all metal bridges are at- 
tached cast-iron name plates giving the name of the com- 
pany constructing the bridge, with date of construction, and 
sometimes other data, such as the names of the officials 
purchasing the bridge, etc. This information is given by 
raised letters cast upon a plate of suitable size. The names 
are formed by attaching the letters in the proper positions 
upon the wooden pattern used in casting the plate. Letters 
are made especially for this purpose and are usually kept in 
stock; they can be purchased at almost any hardware store. 
The name plates are attached by rivets or bolts to conspic- 
uous portions of the bridge; if a truss bridge, they are 
usually attached to the portals or to the end posts. 

It would be well if the guaranteed capacity of the bridge, 
as well as the name of the builder and date of construction, 
were required to be shown on the name plate. 


1702. Wood Hub Guards.—Railings are used for 
two general purposes, namely, for closing the openings 
between the web members of the trusses along the outer 
edges of the roadway, and for hand railings along the outer 
edges of the sidewalk. Railings along the outer edges of 
the roadway, for the purpose of closing the openings between 
the members of the truss, may serve also to protect the 
members from the hubs of passing vehicles. In fact, this is 
commonly understood to be the principal office of these 
railings, and they are generally known by the name of hub 
guards. 

For many county bridges each hub guard consists simply 
of a line of plank attached to the posts of the truss at the 
height of an ordinary wagon hub above the roadway floor. 
This is commonly a 2” X 10” plank, dressed on one side and 


1072. DETAILS,:- BILLS; ANDRES Tinie iio 


painted, and bolted to the posts so that its center will be 
about 24 feet above the roadway floor. In such cases no 
attention need be given to the hub guard in making the 
shop drawings, further than to show bolt holes in the posts 
at the proper distance above the lower chord pins for 
attaching the hub guard, and some arrangement for attach- 
ing it to the hip verticals. If the hip verticals consist 
simply of round or square bars, this attachment will usually 
be a U-shaped bolt or a bolt made in the form of a hook, so 
that it will hook around the hip vertical rod. 
Wood railings, of the form shown in Fig. 339, are some- 
times placed along the outer edges of the roadway. Many 
eve” of the highway bridges in the 
aa central, western, and southern 
RQ | portions of the United States 
| have short trestle approaches, 
and in such cases this railing 
extends along the outer edges 


SSS 














SS 
3 Zs | ; 
Ni « of the roadway across the entire 
Bx : 

aS . bridge and approach. These 


railings are not attached to the 
trusses, but the posts are halved 

































































"6 upon and bolted to the outer 
UD, «6 lines of roadway joists, as 
256%12" Weeliliiil A ec 
Wate ated c= apy iNT es shown. The construction will 
——S |i 2 . 
= Sil = be readily understood from the 
S yh, uy 
a U purnayy |} 
: a | figure. Although commonly 
S Eh, constructed as here shown, 
SSS SL «Cheeses railings are sometimes 


made lighter, the posts being 

4" x 4", the upper railing pieces 

FIG, 339. 2” x 4", and the lower railing 

pieces 2” x 8”. Although this may be called a hand rail, it 
is here noticed under the head of wooden hub guards. 


1703. Iron Hub Guards.—On some county bridges, 
and on most city bridges, iron hub guards are used. In 
some cases, each hub guard consists simply of two lines of 


DETAILS, BILLS, AND ESTIMATES. 1073 


gas pipe, about 2 inches in diameter, attached to the posts 
of the truss. When gas pipe railing is used it is necessary 
only to designate the required size and lengths of the pipe, 
with the couplings, and show the arrangement of the fast- 
enings by which it is attached to the posts. Usually, some 
kind of standard fastenings are used, which simply require 
certain holes to be shown in the posts. 

What is probably the best form of hub guard consists of 
two angle bars latticed. This railing is usually from a foot 
to 18 inches in depth; that is, one angle is placed froma 
foot to 18 inches above the o 
ticing is used, composed 
of light lattice bars mak- 
ing an angle of 45 degrees 
with the angles. The gen- 
eral construction of such 
hub guards, with the. 
splices and _ fastenings, 
must be shown on the 
shop drawings. In Fig. 
340 is shown a portion of 
a latticed hub guard, with tS oad 
the manner in which it is attached to the intermediate post; 
it is composed of two of the lightest 3” x 2” angles, double 
latticed with 1}” x 3” lattice bars. As here shown, it is at- 
tached to the intermediate post by means of short pieces or 
clips of the same size of angle. The design of the hub guard 
is merely a matter of detail; no further explanation will be 
required. 





A double system of lat- 


1704. Hand Rails.— Many different designs are used 
for hand rails, all being more or less ornamental. All-hand 
rails, however, consist essentially of an upper and lower 
horizontal rail, connected by a webbing of lattice or other 
light ornamental work. Sometimes a lighter rail is also 
placed about midway between the upper and lower rails. 

The lower rail will generally consist of two angles, while 
if a middle rail is used it will usually be a single angle. 


1074" DETAILS, BILLS, AND VES EIN a 


The upper rail is made in various forms and is often quite 
ornamental. The top of the upper rail is usually about 
3 feet 9 inches above the sidewalk floor, and the lower rail 
should not be’more than 6 inches above the floor. The 
openings in the lower part of the lattice work should not be 
more than 6 inches square. 

The rails are supported by posts attached to the ends of 
the floor-beams. They should usually be braced at intervals 
of about 8 feet. Both rails are connected and supported at 
each post, but it is quite commonly the case that the lower 
rail only is braced at intermediate points. It will not be 
necessary to show here any designs of hand rails, but it will 
be well to show the manner in which the posts are connected 
to the ends of the floor-beams, because this connection 
forms a part of the engineering design of a structure. The 
posts quite commonly consist of two angles each, but 
sometimes consist of four angles each, and sometimes of 
other forms. 


1705. Attachment of Hand-Rail Posts.—Posts 
are sometimes riveted rigidly to the ends of the floor-beams, 
as: shown vin Hiow3415) 22 his 
forms an excellent attachment, 
so far as the attachment itself 
is concerned, but it is very in- 
convenient for getting the 
upper rail in straight line. 
The attachment not being ad- 
justable, if the rail is not put 
in perfect line before the posts 

Fic. 841. are riveted). Or iit titoneeaies 
cause it should afterwards get out of line, it would be very 
difficult, if not impossible, to put the rail in perfect aline- 
ment. For this reason various adjustable attachments are 
used, by means of which the rail can be lined up without 
difficulty. 

A very common adjustable attachment is shown in Fig. 
342. It consists of ashort brace connecting the post with the 








DETAILS, BILLS, AND ESTIMATES. 1075 


projecting end of one of the lower flange angles. The brace 
passes through a _ hole 
in the flange angle, and 
the attachment is made 
adjustable by means of 
two nuts upon the brace 
screwing against the 
flange. By means of this 
adjustment the top of the 
post may be readily 
thrown in or out and the 
railing be put substantial- 
ly in line before the last 
rivet attaching the post to ' =~ BIGr G83. 
the floor-beam is driven. But even after the post is riveted, 
its top can, to some extent, be 
sprung in or out by this adjust- 
ment. <A simple, compact, and 
efficient adjustable attachment 
is shown in Fig. 343. In this 
attachment, the two angles of 
,the post, passing upon each 
side of the web of the floor- 
beam, are attached directly to 
the web by a single bolt or 
rivet, and, by means of a short headless bolt carrying two 
nuts at each end, the lower end of each angle is attached to 
a short angle clip riveted upon the lower portion of the beam. 
As will be. clearly understood from the figure, the position of 
the post can be readily adjusted by means of these bolts. 








PAINT AND PAINTING. 

1706. General Considerations.—The thorough 
painting of metal bridges is of great importance. “The 
members of iron or steel bridges do not commonly wear out 
from use, although they may be somewhat impaired; but 
they deteriorate very materially through the action of rust. 
Iron or steel exposed to the action of the atmosphere will 


1076 DETAILS, BILLS, AND ESTIMATES. 


soon begin to oxidize or rust, and the process, once begun, 
will continue rapidly. In order to preserve the metal from 
rusting, it must be well protected by paint or other imper- 
vious coating. A paint that will preserve iron work from 
rusting must afford a coating to the surface of the metal 
that is absolutely impenetrable to air, moisture, or gases; it 
must protect the metal perfectly from the destructive influ- 
ence of oxygen, which will combine with it to form rust 
(iron oxide) whenever moisture is present. A paint con- 
sists of a pigment or coloring body, ground and carried in 
suspension in linseed oil or other suitable carrier. The 
value.of the pigment will be the greater the more finely it 
is ground; the greater the proportion of finely ground and 
well-mixed pigment the paint contains, the better it will 
generally be. 


1707. The Kinds of Paint Used.—The kinds of 
paint most commonly used for metal bridges are red lead, 
white lead, asphaltum, iron oxide, graphite, and various 
proprietary or patented mixtures. The relative merits of 
these various paints will be briefly noticed. The amount of 
reliable information on this subject is not great, and there 
exists much difference of opinion concerning it, but the 
statements made below are believed to be fair and, as nearly 
as possible, reliable. 


1708. Red lead is a pure oxide of lead (triplumbic 
tetroxide Pb, O,), and, when mixed with pure linseed oil, 
appears to be the best paint known for preserving iron work 
from rust. When subjected to the severest test this paint 
has shown good results. It is extensively used for painting 
important structures, and is quite generally conceded to be 
superior to all other kinds of paint as a priming coat for 
metal work. 


1709. White lead (%5 per cent. lead carbonate and 25 
per cent. hydrated lead oxide), when pure and mixed with 
pure linseed oil, probably deserves to be classed next to red 
lead as a protective paint. As, however, one of the con- 


DETAILS, BILLS, AND ESTIMATES. LOT? 


stituents of white lead is a hydrated oxide, it is not as suit- 
able a paint for iron work as for wood work; it is not 
extensively used for painting metal work. White lead is 
very commonly adulterated with white clay. 


1710. Asphaltum paint is generally a mixture of as- 
phalt (a solid bitumen or natural pitch) with certain forms 
of lead, minerals, and coloring matter, ground in linseed oil. 
This paint is quite extensively used for painting metal 
structures. Though not generally considered equal to red 
lead as a coating for metal, pure Trinidad asphalt, properly 
prepared and ground in pure linseed oil, forms a durable 
paint for metal work and is commended by its cheapness. 
It is, however, disadvantageously affected by the extremes 
of heat and cold. It is often adulterated with coal tar, 
which is not a good material for paint. 


1711. Jron oxide has been very extensively used for 
painting metal structures. It is used in several forms and 
mixtures, which are known by various names, such as zrvon 
clad paint, armor paint, tron ore paint, mineral paint, mag- 
netic paint, etc. With regard to the chemical composition 
of iron oxide paint, the following may be stated: 

There are three well-defined oxides of iron which occur in 
considerable quantities in a natural state, and may be pro- 
duced artificially; nearly, if not quite, all commercial oxides 
are mixtures of these. The magnetic oxide is generally 
black in color, on which account it is not extensively used 
as a pigment. The anhydrous sesquioxide (red hematite) 
varies in color from a bright red toa dark brown. This is 
the most common oxide of iron. The hydrated sesquioxide 
(brown hematite) is a compound containing a large percent- 
age of water; it often contains also sulphur and other 
organic acids, as impurities. Iron rust 1s a hydrated oxide. 
All iron oxide paint probably contains, or partly consists of, 
hydrated oxide or, practically, iron rust. Moreover, the 
percentage of earthy materials and other impurities in iron 
oxide paint is large. 

It is believed by many that when iron oxide paint is 


1078 DETAILS, BILLS AND BST Ce: 


applied to iron it tends to superinduce corrosion of the sur- 
face coated. Whether this is really the case or not. iron 
oxide paint can not be said to possess great merit as a pre- 
servative of iron. 


1712. Graphite is to some extent used as a paint for 
metal structures. This material is sometimes called ‘‘ black 
lead,” but it is not lead in any form nor similar to lead; it 
is carbon. Graphite is, however, a permanent and neutral 
substance, and is the most indifferent to chemical influence 
of any known pigment. But, asa practical paint, graphite 
possesses certain decided disadvantages. It is so hight that 
it is impossible to get any considerable percentage of it 
into the oil, and it is also flaky and greasy, partaking rather 
of the nature of a grease than of a true paint. Although 
graphite doubtless possesses considerable merit as a paint, 
it is said not to be impervious to water nor have sufficient 
body to be a really efficient preservative of metal work. 


1713. Proprietary or patented paints are generally not 
tovbe relied’ upon. “As theirtingredientseare ke pteecea. 
little can be said concerning them, except that all secret 
mixtures are to be looked upon with suspicion until their 
merit or lack of merit has been fully proved. For iron work, 
at least, it is a good rule never to use paint purchased upon 
the market in a ready-mixed form as prepared paint. (As- 
phaltum paint may, however, be considered as a possible 
exception to this.) Several mixtures of this kind, when 
analyzed, have been found to contain large percentages of 
such adulterants as carbonate of lime, red ciay, etc. It 
must be conceded, however, that certain proprietary paints 
have been found quite efficient for protecting iron work. 

From what has been said it may be concluded that the 
most reliable paints for metal work are red lead and asphal- 
tum. Of these, red lead is the better, while asphaltum is, 
in its first cost, the cheaper. Red lead is believed to be the 
best paint that can be used for the priming coat on iron 
work. Other paints, however, are sometimes preferred for 
the outside or finishing coat. 


DETAILS, BILLS, AND ESTIMATES. 1079 


1Z714. Covering Capacity of Paints.—When used 
under ordinary conditions, the covering capacity of the 
common kinds of paint is reasonably well known. By the 
term covering capacity is meant the amount of surface 
that can be covered by a certain amount of paint; as usually 
expressed, it is the area, in square feet, that can be cov- 
ered by a gallon of paint. For thé various kinds of paint 
mentioned above, used on new work with the average con- 
ditions of surface, the covering capacities will generally be 
about as given in the following table: 


TABLE 45. 


AREA COVERED BY ONE GALLON OF PAINT. 























Area in Square Feet. 
Kind of Paint. e ' 

First Coat.) ~<°0"* 

Coat. 

OS IER OEMs ON 9a i 700 1,000 
White lead, iron oxide, or graphite.... 500 700 
We Cy eB AE fa 2) ties nn a a 300 500 











The covering capacity given for red lead is for the mix- 
ture known as the B. & O. Railroad formula; namely, ten 
ounces of lampblack to twelve pounds of red lead. The 
resulting paint is a very dark brown, nearly black. For 
repainting old work, the covering capacity of the first coat 
will generally be about half as much as for the first coat on 
new work. 


1715. The Use of Red Lead.—Red lead should 
always be purchased as adry paint, mixed with pure linseed 
oil, and used when freshly mixed. A mixture of pure red lead 
and linseed oil partakes somewhat of the nature of a soap or 
cement; it will ‘‘ take a set” in a few days. This ‘“‘setting ” 
of red lead mixed with linseed oil is, by some authorities, 
spoken of as saponification, but Professor Spennroth, of 
Aix-la-Chapelle, states that he has proved by numerous 


1080 DETAILS, BILLS, AND ESTIMATES: 


experiments that saponification does not take place with any 
of the usual pigments. However this may be, on account 
of its setting quality, red lead can not be sold as a mixed 
paint; it should always be mixed fresh each day as used. 
Red lead paint a day old, or which has begun to set, should 
not be used. 

Red lead combines more perfectly with linseed oil when 
the raw (unboiled) oil only is used, but, on account of the 
weight of the lead, such paint must be mixed very thick in 
order to prevent the particles of lead from settling in the 
vessel or ‘‘running’”’ on the painted surface. . It shouldbe 
used as thick as may be expedient. When the mixture is 
desired to be thinner than is obtainable with raw oil alone, 
a small quantity of japan should be used, or boiled oil may 
be used instead of raw oil. 


1716. Proportions for Mixing Red Lead Paint. 
—For painting iron work, the proportion of red lead to 
linseed oil may be from 3 to d parts of red lead to 1 part of 
linseed oil dy wezght, or say from 24 to 40 pounds of red 
lead to each gallon of linseed oil. About 4 to 1 by weight, 
or say 30 pounds of red lead to 1 gallon of linseed oil, is a 
good average mixture. If mixed in about this proportion, 
20 pounds of red lead in 55 pounds (.7 of a gallon) of linseed 
oil will make a gallon of paint. When japan is used asa 
dryer, there should be, by either weight or measure, about 
one part of japan to 10 parts of linseed oil. 

The color of red lead mixed with pure linseed oil may be 
described as a bright brick red, or about midway between a 
bright vermilion and a terra cotta. When a darker shade is 
desired, it can be obtained by adding a small amount of 
either lampblack or graphite. One-sixteenth of an ounce 
of lampblack to one pound of red lead will produce a rich 
chocolate color, while an ounce of lampblack toa pound of red 
lead will produce a very dark brown, scarcely distinguishable 
from black. 


1717. Amount of Painted Surface.—In bridges of 
different forms, the amount of surface to be painted will 


DETAILS, BILLS, AND ESTIMATES. 1081 


vary through a considerable range; it will not be exactly or 
very closely proportioned to any fixed dimension of the 
bridge, and, therefore, can not be accurately expressed bya 
formula. Some forms of trusses will have an area of painted 
surface much greater than others of the same span and 
capacity. The most reliable practice is to estimate the 
actual amount of surface to be painted in each case, although 
this involves an amount of labor that is not usually warranted 
by the importance of the result. 

For ordinary Pratt truss bridges, however, carrying a 
single roadway, the following formulas are probably as sat- 
isfactory as any that can be proposed. 

For highway bridges of 16 feet roadway and a live load 
capacity of 90 pounds per square foot: 


A=~<(L—2) +400 (265.) 


For single track railroad bridges of 80 feet span and over: 


B 


A=4l (= 


+1) (266.) 
In both of which A is the total area of painted surface in 
square feet, and Z is the length of span in feet. 


1718. Preparing Iron for Painting.—Before iron 
work is painted it should be thoroughly cleaned of all rust, 
scale, anddirt. Zs 7s of great importance, and should never 
be neglected. It is probable that an ordinary quality of 
paint on well-cleaned iron will more effectually preserve 
the metal than the best quality of paint upon a rusty surface. 
The progress of the oxidizing or rusting process, when once 
begun, may be somewhat checked by the application of paint, 
but it can not be stopped by it. The rusting process will 
continue slowly under the paint until the latter will peel off 
with a layer of rust. Although the progress of the rusting, 
when once begun, cannot be prevented by paint, it will 
probably be as well opposed by red lead as by any paint. 

New iron work, before being painted, should be well 
cleaned. All loose scale, dirt, and rust should be removed. 


1082 DETAILS, BILLS, AND ESTIMATES: 


Wire brushes are used for this purpose. Cooper's specifica- 
tions require that ‘‘all iron work before leaving the shop 
shall be thoroughly cleaned from all loose scale and rust, 
and be given one good coating of pure raw linseed oil, well 
worked into all joints and open spaces.”” This specification 
is often but indifferently complied with. 

Pure raw linseed oil is specified for the priming coat be- 
cause to some extent it allows the condition of the surface 
of the iron beneath it to be seen during the construction 
of the work and before the application of the second coat. 
Except that it removes all opportunity for subsequently in- 
specting the condition of the surface of the metal, red lead 
mixed with raw linseed oil forms a much better priming 
coat for iron work than the linseed oil alone. 

A surface of rusting iron, or one covered with old decom- 
posing paint (on which more or less rust is always present), 
will require more thorough treatment. Such a surface may 
sometimes be cleaned by a thorough and vigorous applica- 
tion of wire brushes. But, if the surface is considerably 
rusted, it may be necessary to use kerosene ora dilute solu- 
tion of sulphuric or muriatic acid in connection. with the 
wire brush treatment. A badly rusted surface should be 
well scrubbed with water containing about 25 per cent. of 
muriatic acid or about 3 per cent. of sulphuric acid, after 
which it should be well washed with lime water to neutralize 
the acid, then thoroughly dried before painting. 


IMPERFECT DESIGN AND INCONSISTENT 
REQUIREMENTS. 


1719. The design of all details of the bridge shown on 
the Mechanical Drawing plates, and certain features of 
bridge design not there shown, have been explained. Many 
of the details shown in those drawings are not the best 
details possible, and they do not, in all cases, comply with the 
requirements of the specifications. This design was made 
for the purpose of instruction in Mechanical Drawing, and 
for convenience was used to illustrate the principles of 


DETAILS, BILLS, AND ESTIMATES. 1088 


bridge design as taught in this Course; it is not given as an 
example of perfect design. It will be very instructive to 
notice now a few of the imperfections of this design. 


1720. Light Weights and Thin Metal.—In this 
design, the lightest weights of 8-inch channels (10 pounds per 
foot) are used for the upper chord. The metal in the webs 
of these channels is about 34 (.21) of an inch in thickness, 
whereas, according to the specifications, no metal should be 
less than 4 of an inch in thickness. ‘These channels should 
be of such weight as would give 4 of an inch thickness of 
metal in the web. The increase of the weight, correspond- 
ing to the required increase in the thickness of the web, may 
be calculated by formula 174, Art. 1555. The required 
increase in the thickness of the web is .25 — .21 = .04 of an 
inch, and, by applying this formula in the present case, we 


shall have the equation fy ES from which y=1.07 


8 
pounds. The weight per foot of each channel in the upper 
chord should, therefore, be 10+ 1.07 = 11.07, or say 11 
pounds per foot. 

In making a design, it is a good plan to use, so far as pos- 
sible, shapes in which the thickness of metal in the lightest 
weights rolled is not less than the minimum thickness allow- 
able, which is usually }of an inch. But when the thickness 
of metal used is less than 4 of an inch, it should not be 
counted as + of an inch in computing the bearings upon the 
pins and rivets, as is not infrequently done. It is exceed- 
ingly bad practice to use metal less than 4 of an inch in 
thickness for any important part of a member. 


1721. Countersunk Rivets.—Rivets should not be 
countersunk in metal having a thickness less than one-half 
the diameter of the rivet; rivets of an inch in diameter 
should not be countersunk in metal less than ;%, of an inch 
thick. As the webs of the channels in the upper chord are 
less than ;%, of an inch in thickness, the rivets in them 
should not be countersunk. At the hip joint, the rivets 
nearest to the pin in the pin plate should be located at a 


1084 DETAILS, BILLS, AND ESTIMATES. 


sufficient distance from the pin to clear the ends of the pin 
plates on the end post without being countersunk. Coun- 
tersunk rivets are not, in any case, as reliable as rivets with 
full heads, and are move expensive; they should be avoided 
where possible. 


1722. Unsymmetrical Sections.—Symmetrical sec- 
tions should be used for compression members whenever 
possible. It is a very general practice, however, to use un- 
symmetrical sections for top chords and end posts, and 
there are some advantages in using them. In some cases 
symmetrical sections composed of two channels latticed on 
both sides are used for these members, but much more 
commonly a cover-plate is attached to the upper flanges of 
the channels, while the lower flanges are stayed by lattice 
bars, thus forming an unsymmetrical section. In case the 
section is so heavy that it has to be composed of plates and 
angles, the angles forming the lower flanges can often be 
made enough heavier than the angles of the upper flanges 
to counterbalance the section of the cover-plate. This will 
give a section which, though not symmetrical in form, is not 
eccentric with reference to the position of its center of 
gravity, and may be treated as a symmetrical section. 

In any compression member connecting upon pins, the 
pins should be located in such position that the stress upon 
the member will be uniformly distributed over its section. 
If the member is not vertical, the bending stress due to the 
weight of the member itself must be considered in fixing 
the position of the pins, as was explained in Art. 1498. 
When this is done, further consideration of the bending 
moment, due to the weight of the member only, may be 
neglected. 


1723. Eccentricity of Pin Plates.—One serious 
disadvantage of chord sections in which the pins are not at, 
or very near, the centers of the channels or side plates, is 
that the bearings upon the pin plates are generally eccentric 
with reference to the rivets attaching the pin plates. This 
produces a sidewise bending movement upon the pin plate, 


DETAILS, BILLS, AND ESTIMATES. 1085 


which, although it has no very injurious effect upon the 
plate, increases the stresses upon some of the rivets. It is 
possible to obtain a satisfactory solution for the intensities 
of the stresses upon the rivets, but, as the solution is rather 
complex, it is doubtful whether it would be worth while to 
apply it to the rivets of ordinary pin plates, and it will not, 
therefore, be given here. In practice, the number of rivets 
in a pin plate should be increased somewhat when the pin 
bearing upon the pin plate is eccentric. When the pins in 
a member are but slightly eccentric, the positions of the 
rivets in the pin plate, with reference to the pin, can usually 
be so arranged that the pin bearing will not be eccentric 
with reference to the rivets. 


1724. Pitch of Rivets at Ends of Members.— 
The specifications require that ‘‘the pitch of rivets at ends 
of compression members shall not exceed four diameters of 
the rivets for a length equal to twice the width of the 
member.” 

This requirement was not strictly complied with in the 
rivet spacing on the chord and end post of the bridge con- 
sidered. The rivet spacing on these members could be con- 
siderably improved by being made more uniform and being 
also made to comply with the requirements of the specifica- 
tions. All rivet spacing should be as regular and uniform 
as possible; itregular spaces should be avoided. 


1725. Requirements for Fatigue of Metals.—In 
Art. 1466, it was noticed that some specifications take the 
fatigue of metal into consideration in determining the 
allowed unit stresses. It appears from the experiments of 
Spangenberg that it is in the case of alternating stresses 
only that the material fails from repetition of stresses below 
the elastic limit; the material does not fail from repeated 
stresses of the same character, so long as they do not exceed 
the elastic limit. As the unit stresses allowed are always 
well within the elastic limit of the material, it is evident 
that for stresses of the same character the fatigue of the 
metal may be neglected. 


1086 DETAILS, BILLS, AND ESTIMATES. 


But for stresses alternating between tension and com- 
pression, the material is found to fail under stresses con- 
siderably below the elastic limit, if repeated a sufficiently 
great number of times. Consequently, for this condition 
the fatigue of the metal should always be considered. 


1726. Requirements for Flat-Ended Columns.— 
In some specifications greater unit stresses are allowed for 
flat-ended columns than for pin-ended columns, and this is 
avery common practice. Theoretically, flat-ended columns 
are stronger than pin-ended or round-ended columns of the 
same dimensions; from experiments also this is found to be 
the case when the bearings of the flat-ended columns are 
perfect, and the load upon them is symmetrical with refer- 
ence to their neutral axes. But when the bearings of a flat- © 
ended column are imperfect, or when from any reason the 
load upon the column becomes eccentric, the flat - ended 
column may be even weaker than a round-ended column of 
the same dimensions. A pin-ended column is practically 
round ended with reference to a plane perpendicular to the 
axis of the pin. 

The load upon a properly constructed round-ended column 
will be applied at its neutral axis, and the stresses will be 
uniformly distributed over its section, while the load upon 
a flat-ended column will nearly always be more or less 
eccentric. The eccentricity of the load produces a bending 
moment upon the column; the latter, must, therefore, 
resist the bending moment as well as the actual compression. 

Thus, it is seen that while a flat-ended column is stronger 
than a round-ended column when perfect conditions of load- 
ing are attained, it may be weaker when perfect conditions 
are not attained. As the conditions of the bearings in flat- 
ended compression members are usually such that the mem- 
bers are loaded more or less eccentrically, it is evident that 
flat-ended compression members can not consistently be 
allowed greater unit stresses than pin-ended members. 

In a bridge, some of the compression members may be 
allowed higher unit stresses than others, according to the 


DETAILS, BILLS, AND ESTIMATES. - 108" 


general form of their connections, their liability to eccentric 
loading, and the nature of their stresses. For bridge work 
it is probably the best practice to treat all columns as pin- 
ended, and, in specifying the allowed unit stresses, designate > 
the members to which they apply. 


CONCLUDING REMARKS. 


1727. The design of a structure should be simple; it 
should, as far as possible, conform to the requirements of 
the stresses, and be complete in every detail. Each part 
and detail of a structure should be strong enough to bear 
alone the stress for which it is intended. The structure as a 
whole can not be stronger than its weakest part, and it is 
useless to make one part relatively stronger than another. 

Each detail should not only have the required strength, 
but it should be simple and practical. At each joint where 
several members connect, the connections should, if possible, 
be so designed that the axes of all the connecting members 
shall intersect at a common point. The designing of such 
- details requires skill, judgment, and experience, as well as 
careful consideration of all the conditions attending each 
case. Each detail should be well studied and made assimple 
and practical as possible, having in mind the economical re- 
quirements of the shop work and erection. The simplest 
details are the most difficult to design. 

Where there are several similar details they should, if pos- 
sible, be made alike, as the shop work is thereby much 
facilitated. Familiar details should generally be used. In 
nearly every bridge office certain standards of construction 
are adopted. These should be used whenever practical, be- 
cause the shop men are familiar with them, but a good detail 
should never be sacrificed for the sake of using a standard. 

The shop drawings should be so made as to be readily un- 
derstood by the workmen. All letters, words, and figures 
written on them should be plain and easily read. In making 
shop drawings it must be borne in mind that they are for 
the purpose of conveying exact information to the shop men, 


1088 DETAILS, BILLS, AND ESTIMATES. 


who are not supposed to have, and generally have not, any 
knowledge concerning the structure other than that obtained 
from the drawings. The information given on the drawings 
must, therefore, be complete and explicit. 

Information once given should generally not be repeated; 
dimensions or rivet spacing shown on a top or bottom view 
should not be again shown on the side elevation. Such 
repetitions not only require unnecessary labor upon the 
drawings, but tend to confuse the workmen. Where two 
members are exactly alike except that the positions of cer- 
tain corresponding dimensions are reversed, as the portal 
connections on two end posts, it is sufficient to show the di- 
mensions in one position and mark the members vzg/t and 
left. It is generally sufficient to show half top and half bot- 
tom views of chords and end posts; in such cases they are 
shown together in one half top and half bottom view, both 
being shown as seen from above. The lower ends of ver- 
ical and diagonal-members should generally be at the left on 
the drawing. 

No computations whatever should be left for the workmen 
to do; every necessary calculation relating to a structure 
should be performed in the office. The workmen will do well 
if they properly carry out the construction according to the 
drawings. Although the dimensions for any part of a bridge 
are never taken by scale from the working drawings, the 
scale, together with the title and date, should, for conve- 
nience in the office, be given in the lower right-hand corner 
of each drawing. 


STREETS AND HIGHWAYS. 





COUNTRY ROADS AND HIGHWAYS. 


GENERAL CONDITIONS. 

1637. City Streets and Country Roads.—The 
difference between country roads and city streets is largely 
a difference of quality and condition; the principles under- 
lying their proper location, construction, and maintenance 
are essentially the same for both; but, as the application 
of those principles is simpler in the case of country roads, 
the latter will be considered first. 


1638. What Constitutes a Good Road.—A good 
road is easily recognized in driving over it, yet the con- 
ditions necessary for a road to be a good one are not very 
generally understood. It will be well here to notice these 
conditions, in order to determine what things are to be 
obtained,and then we may consider the problem of how to 
obtain them. 

In order that a road may be satisfactory for public travel, 
it should be dry, solid, of easy grade, and smooth, Other 
conditions may be, and usually will be, desirable, but these 
conditions are essential. They are named in the general 
order of their relative importance. 


1639. A Good Road Must Be Dry.—This is very 
important. A water-soaked road can not be good, and a 
road that will retain water on its surface will soon become 
water-soaked. A road composed of light, porous sand 
_will be firmer and better when moist than when thoroughly 
dry, but it will not retain water on its surface, and will 


For notice of copyright, see page immediately following the title page. 


996 | STREETS AND HIGHWAYS. 


not become water-soaked, because the water will rapidly 
percolate through it. In other words, such a road is self- © 
draining. For all other kinds of roads, thorough drainage 
must be provided, so that they will not become water- 
soaked in any kind of weather. 


1640. A Good Road Must Be Solid.—The material 
of which a roadway is constructed should be such that it 
can be thoroughly compacted, so as to sustain the travel 
ona firm, unyielding surface, and without the formation 
of ruts. The resistance to travel will be small on such a 
road, while on a soft road, or a road cut up with ruts, the 
resistance will be great. With almost all materials used 
in road making, a solid road may be maintained without 
great difficulty, if the drainage is thorough. 


1641. A Good Road Must Have Easy Grades.—A 
road may be otherwise good, and still be of comparatively 
little value as a public highway, by reason of its steep 
grades. Such grades limit not only the loads that can be 
hauled over the road, but also the speed of travel, without 
any compensating advantage. A grade that is so steep 
that a descending vehicle must be held back by brakes or 
otherwise is too steep, as the energy expended by the 
brakes or by the holding back of the team is simply 
wasted. There is a corresponding expenditure of energy 
in ascending the grade that would not be necessary 
on an easier grade. In almost every case, excessively 
steep grades can be avoided by a judicious location of 
the road. 


1642. A Good Road Must Be Smooth. — Roads may 
be dry and solid, and have easy grades, and still be quite 
unsatisfactory because of their roughness. The roughness 
may be due to uneven piaces in the surface, or merely to 
loose stones lying in the roadway. Whatever the cause, it 
is a very undesirable condition, which is both annoying and 
detrimental to travel; although it not uncommonly exists, 
there 1s no reason for it except negligence. 


STREETS AND HIGHWAYS. 99 
LOCATION OF HIGHWAYS. 


GENERAL CONSIDERATIONS. 


1643. Importance of Proper Location.—A matter 
of the first importance relating to the subject of highways 
is that of their location. This involves a consideration of 
their alinement and their grades. Although these subjects 
are both of great importance, they are seldom properly 
considered in determining the locations of roads. 

The subsequent value of a road, as a public thoroughfare 
and means for transportation, will depend largely upon the 
judicious and proper location of it with reference to its 
alinement and grades. The grades of a road will not only 
directly limit the speed of travel and the magnitudes of the 
loads that can be hauled upon it when in a given condition, 
but, by influencing the conditions relating to drainage, they 
will, indirectly and to no inconsiderable extent, affect the 
condition of the roadway also. A road properly constructed 
and maintained, will be, to a large extent good or bad ac- 
cording as its grades are favorable or unfavorable. The 
grades should be the paramount consideration in the loca- 
tion-of a road, and the alinement should be, so far as pos- 
“sible, such as to give the most favorable grades and efficient 
drainage. 


1644. Location of the Older Highwayss—Many 
of the older roads of the country were constructed along 
former emigrant trails and roads cut through the wilderness 

~ from one settlement to another. The construction of these 
roads followed the general development of the country, and 
was in no sense systematic. As is to be expected from the 
circumstances, such roads were not always located in the 
best possible positions, and, in many cases, the locations 
were quite unfortunate. While this is to be regretted, 
yet it is the legitimate result of the conditions attend- 
ing the settlement and development of our country, 
and can not now be remedied without relocating the 


roads, 


998 STREETS AND HIGHWAYS. 


1645. Common Modern Practice of Road Loca- 
tion.—In the location and construction of the public high- 
ways through the country at the present day, however, the 
conditions are entirely different, and the public have a right 
to expect that these roads shall be properly located, and con- 
structed in the best manner possible with the means at hand. 
But this is rarely ever done. A highway constructed from 
one place to another through the country is almost always 
located either upon an approximately straight line, or along 
the division lines between properties. The matter of grades 
usually receives very little consideration, except where the 
slopes become so steep as to be almost, or quite, prohibitory ; 
the matter of drainage is seldom considered at all. 

As arule, the men who lay out these highways are not 
engineers; they neither understand nor appreciate the 
engineering features involved, and think that all essential 
conditions are fulfilled if the road is reasonably direct be- 
tween terminal points, and is located in such a position as 
to be satisfactory to the property owners along the. route. 
Whether the route is over hills and through swamps is a 
matter they usually disregard, and they are satisfied if the 
road occupies the least valuable land and adheres as closely 
as possible to property lines. This practice is radically 
wrong and should be abandoned. 

The value of country property is affected to no inconsid- 
erable extent by the condition of the roads leading to the 
market towns, and it is greatly to the interest of property 
owners that these roads be constructed and maintained in 
the best manner consistent with a reasonable expenditure. 
This end can be attained only by good engineering in the 
location and construction, and by intelligent supervision in 
the maintenance. 


1646. Highway and Railroad Locations Com- 
pared.—lIt is quite safe to state that, had the railroads of 
this country been located in the same manner as the high- 
‘ ways, comparatively few would have been built and success- 
fully operated. The principles underlying the proper 


o 


STREETS AND HIGHWAYS. 999 


° 


location of a highway are much the same as those upon 
which the location of a railroad is based, and there is no 
sufficient reason why the location of highways should not 
also be based upon principles of sound engineering and 
common sense. In railroad location, the obtaining of favor- 
able grades and thorough drainage are recognized as among 
the chief conditions of a good road, and the location and 
alinement of the road are made largely subservient to these 
ends. These should be the chief considerations in the loca- 
tion of highways also, although considerably steeper grades 
are practicable for highways than for railroads. 


1647. Considerations Relating to Alinement 
and Grades.—In locating a highway through the country, 
its alinement should be such as to give the best available 
grades, and afford thorough drainage. If sufficient care and 
judgment are exercised in the location, excessive grades can 
usually be avoided. In the majority of cases, it is much 
easier to go around a hill than to go over it, and a ju- 
diciously selected route around the hill will not usually be 
much longer than the route directly over it. For, while the 
route around the hill will deflect laterally from a straight 
line, the route over the hill will deflect from it vertically, 
and the difference in length of the two routes will not gen- 
erally be very great. When impossible to avoid crossing a 
hill or ridge of high ground, the crossing should be made by 
devious courses and easy grades, rather than by a direct 
course and steep grades. The hauling power of a team is so 
much greater on easy grades than on steep grades that it 
more than compensates for the difference in distance. 

For a given load, the work required to overcome a rise of 
one foot will be equivalent to that required to haul the same 
load, on a perfectly level road, a distance of from about 
" to 22 feet on an earth road, 15 to 30 feet on a gravel road, 
and 30 to 40 feet on a macadam road,* according to the con- 
dition of the roadway surface. Moreover, on steep grades, 


* These may be taken to be about the usual ranges of values, though 
the actual values may, in some cases, vary above or below these limits. 


1000 STREETS AND HIGHWAYS. 


the roadways are damaged much more by storms than on 
easy grades. During a single storm, the storm water flow- 
ing violently down a steep roadway may cut out deep chan- 
nels and seriously damage it. On the other hand, a perfectly 
level grade is seldom desirable for a roadway, because, unless 
the roadway is situated along a side hill, the opportunity for 
efficient drainage will not be afforded. 

Where there is no reason for deviating from a direct 
course, the road should be made~as direct as _ possible 
between the points which it is to connect. Due regard, 
however, should always be given to the matters of grade 
and drainage, which are of much greater importance than 
direct alinement. In northern climates, roads leading from 
valleys to higher ground should preferably be located on 
slopes facing the south or west, where they will be most ° 
protected from storms and snowdrifts during the winter, 
and soonest clear of snow in the spring. 


RECONNAISSANCE AND SURVEYS. | 

1648. Examination of Country.—A highway 
should be located in practically the same manner asa rail- 
road, although the conditions to be fulfilled are not nearly 
so rigid. As one of the first steps, the locating engineer 
should go over the entire route on foot and carefully study 
all itsfeatures. He should become thoroughly familiar with 
the country traversed, and his study of the route should be 
s0 thorough as to practically determine the position of the 
line. 

The work will be much facilitated by having a reliable 
map of the territory traversed. If a good topographical map 
is available, the approximate position of the line may be 
determined with reasonable certainty before going into the 
field. The amount of work necessary to be expended upon 
a reconnaissance will depend upon the difficulties attending 
each particular case, but it should always be sufficient to 
select the best possible route. 

In some cases, rough measurements should be taken, in 
order better to determine the practicability of the route and 


STREETS AND HIGHWAYS. 1001 


from which to construct a rough map where none exists. 
Courses may be measured with a pocket compass, and dis- 
tances may be estimated by the eye, or by the aid of a 
pedometer. Differences of elevation may be estimated by 
means of an aneroid barometer and by a hand level. The 
Jatter instrument will also be useful in estimating slopes. 
From such measurements, much valuable information may 
be obtained. 





1649. Selecting the Route.—The terminal points 
and those points through which the line must necessarily 
pass must first be determined. Such points will be 
towns, villages, and other centers of population or com- 
merce, passes between mountains, and the most favorable 
points for bridging large streams. These will be fixed 
points from which the line must not deviate. Between 
these points, the best possible route should be selected, with 
reference to easy grades, thorough drainage, and suitable 
material for the roadbed. The route should be as direct as 
practicable, and should first be selected without any regard 
whatever to property lines. 

After the route has been selected, howev Br Cas eas 
of land boundaries should receive pineideracon, though, 11 
some cases, this may be deferred until after a REED, 
line has been run. It will usually be found that, in many 
places, the route of the highway can be so adjusted as to 
follow the division lines between properties without serious 
disadvantage. Thisshould be done, where possible, without 
detriment to the line, as it will usually be much more satis- 
factory to the property owners, but such adjustment should 
not be made to the serious injury of the route. 

It is not essential that the route selected should be even 
approximately straight. Angles may be made wherever the 
conditions require them. In this respect, the location of a 
highway differs materially from the location of a railroad. 
Angles in a highway should not be made unnecessarily, how- 
ever, as a reasonably straight roadway presents a much more 
pleasing appearance than one having many turns and angles, 


T, IV,—t13 


1002 STREETS AND. HIGHWAYS: 





1650. Running and Marking the Line.—When 
the reconnaissance has been made and the general route 
selected, the line should be run withatransit. If necessary, 
in order to select the best route, more than’one line should 
be run, and the most favorable line adopted. The line 
run should be the center line of the highway. Stakes should 
be set on this line at the end of each interval of one hundred 
feet, and numbered consecutively, beginning with zero at 
the starting point. Each point so marked and numbered is 
called a station. A transit hub should be driven at each 
angle in the line, and the exact position of the point should 
be fixed by a tack driven in the top of the hub; its position 
along the line should be designated by the number of feet, 
called the plus, from the preceding station. 

The position of each point at which an angle occurs in 
the line finally adopted should be fixed upon the ground by 
measurements to permanent objects, or to reference stakes 
set outside of the limits of the roadway to be graded, so that 
after the construction of the road the exact point can readily 
be relocated. After the road is constructed, this point 
should be marked by a long stone, or other enduring monu- 
ment, set deep into the ground. The position of this 
monument should be fixed by measuring and recording 
the courses and distances to two or more witness trees, or 
other permanent objects. If the line constructed is thus 
well marked, much annoyance and uncertainty will be 
avoided with regard to the position of the line in after 
years. 

The station and plus at which the surveyed line intersects 
each section line, land boundary, stream, railroad, or exist- 
ing highway should be carefully noted. Where the surveyed 
line crosses each section line, it should be tied by measure- 
ment to the nearest section or quarter-section corner. The 
positions of the initial and terminal points of the surveyed 
line should be fixed by measuring the course and distance to 
the nearest corner of the Government land survey; when 
convenient, it will be well to fix each point by measurements 
to two different corners. 


STREETS AND HIGHWAYS. 1003 


GRADES. 

1651. Levels and Grades.—Levels should be taken 
along the line thus located and marked. In taking the 
levels, notes should be made of all important topographical 
features, such as the position and size of watercourses, the 
timber, the character of the surface, and especially the 
character of the soil. From the levels taken, a profile of 
the line should also be made in practically the same manner 
as in railroad location. The important topographical 
features of the country should be noted on the profile. By 
means of the profile thus made, the available grades should 
be carefully studied, the maximum rate of grade fixed upon, 
and the grade line established. 


1652. The grade line is the line representing the 
surface of the finished roadway, from which may be deter- 
mined all elevations along the same. It is usually shown 
by a red line on the profile. 

While the route is being located, the profile should be 
made and the grade line fixed each evening for that portion 
of the line run during the day. For it will sometimes be 
found that the line located during the day, or some portion 
of it, will prove to be so unsatisfactory with regard to the 
obtainable grades that it will be necessary to relocate it. 
This condition will be definitely shown by the profile, and 
if the making of the profile thus progresses daily with the 
locating of the line, the unsatisfactory portion of the line 
can be relocated the next day before proceeding. 


1653. The rate of grade, or the gradient, is the 
rate of rise or fall along the grade line. The rate of grade 
may be expressed as the amount of rise or fall in a unit of 
horizontal length, in a hundred units of horizontal length, 
or in any given horizontal distance, as in one mile. It may 
also be expressed as a vulgar fraction; when so expressed, 
the amount of rise or fall in any given horizontal distance 
is written as the numerator, and the horizontal distance in 
which the rise or fall occurs is written as the denominator, 
both being in the same unit. When the rate of grade, 


1004 STREETS AND HIGHWAYS. 


expressed as a vulgar fraction, is reduced to the form of a 
decimal fraction, it will express the amount of rise or fall per 
horizontal unit, and will correspond to the sine of the slope. 
(See Art. 1478.) The rate of grade is very commonly 
expressed by the amount of rise or fall per hundred units; 
when so expressed, it is called the rate per cent,.. The 
rate per cent. of a grade is, therefore, the number of units of 
rise or fall in each hundred units of horizontal distance. 

In writing the rate of grade, it is customary to indicate a 
rising grade by a + sign, and a falling grade by a — sign. 
Thus, a grade rising 2 feet in a horizontal distance of 100 
feet would be marked on the profile + 2.00%. The4%sign is 
not uncommonly omitted. 

All computations relating to rates of grade may be based 
upon the following simple 


RULES: 
I. Zhe rate per cent. of a grade ts equal to tts total rise 
or fall in any given horizontal distance divided by the hort- 
zontal distance and multiplied by 100. 


It. he total rise or fall of a grade line in any given 
horizoutrl distance ts cqual to the rate per cent. of grade 
multiplied by the horizontal distance and divided by 100. 


Wi. he horizontal distance in which a grade line hav- 
mga given rate per cent. will rise or fall a certain amount, 
ws equal to the amount of rise or fall divided by the rate per 
cent. and multiplied by 100. 


EXAMPLE 1.—What is the rate per cent. of a gradc that rises 12.24 
feet in a horizontal distance of 450 feet ? 
SOLUTION.—By rule I, the rate per cent. will be cqual to 


12.24 x 100 


750 = 2.12 per cente Ans. 


EXAMPLE 2.—What is the total fall in a grade line ina horizontal 
distance of 648 feet, the rate of grade being — 4.25 per cent.? 


SoLuTION.—By rule II, the total fall will be equal to 


— 4.25 x 648 
— On 
100 = — 27.54 feet. Ans. 


STREETS AN Dy HIG WAYS. 1005 


EXAMPLE 3.—In what horizontal distance will a grade line having a 
rate of + 2.00 per cent. rise 10.64 feet ? 


SOLUTION.—By rule III, the horizontal distance will be equal to 


10.64 « 100 


a, Pp oro “ 
500 hee feet. | Ans 


1654. Maximum and Minimum Grades.—The 
steepest grade on a route is commonly spoken of as the 
maximum grade, and, likewise, the flattest grade on 
the route, that is, the grade approaching most nearly toa 
level grade, is commonly called the minimum grade, 
These respective terms are also applied to those grades that 
have been decided upon as the steepest and flattest grades 
fermissible upon the route. The maximum and minimum 
grades upon the route will generally be the same as 
the maximum and minimum permissible grades. The 
grade adopted as the maximum permissible grade is 
sometimes called the ruling grade. With reference to 
the maximum and minimum rates of grade, the terms 
Maximum gradient and minimum gradient are also 
used. 

In locating a highway, a certain maximum grade should 
be fixed upon, and the route should be so located that this 
maximum grade will not be exceeded. On any portion of 
the line, however, any grade not exceeding this maximum 
grade may be used. ‘The easiest grades should be used on 
those portions of the road where the travel is heaviest, and 
the steepest grades where there is the least travel. If the 
road leads to a large city or market town, the grades near 
the city should be easier than at points more remote, 
because the traffic near the city will be greater in amount 
and heavier in character than at remote points. 

The maximum grade should not be steeper than 9 per 
cent. for earth roads, 64 per cent. for gravel roads, and 3 
per cent. for macadam roads, in any case where possible to 
keep within those limits, and, preferably, should never be 
steeper than about 3 to 5 per cent. for any kind of road. In 
order that efficient drainage may be provided for the road- 
way, the minimum grade should not, in ordinary cases, be 


1006 STREETS AND HIGHWAYS. 


flatter than 1 per cent., and should never be materially 
flatter than one-half of 1 per cent., except on first-class 
pavements. 


COMPARISON OF ROUTES. 

1655. Conditions to be Compared.—Where it has 
been found necessary to run more than one line in order to 
select the best route, the profiles of the different lines will 
afford a fair basis of comparison. The principal conditions 
to be considered in comparing the routes are as follows: 


1. Convenience to Traffic.—The road should, so far as 
possible, be located in sucha position as to accommodate 
those who are to travel upon it. The route that will best 
accomplish this, and, at the same time, afford equal advan- 
tages with regard to the other essential conditions, will be 
the best route. 


2. Short and Direct Route.—All other conditions being 
equal, the shortest route will, of course, be the best. 


3. Lasy Grades.—The route having the easiest grades 
will be the best, other conditions being equal. 


4. Small Rise and Fall.—The route having the smallest 
total amount of rise and fall will offer the least fo¢a/ resist- 
ance to traffic, irrespective of the steepness of its grades. 
Hence, with all other conditions equal, such a route will be 
theese, 


5. Lhorough Drainage.—The route selected should have 
such position and such grades as to afford the opportunity 
for thorough drainage of the roadway. This condition is 
not usually difficult to obtain, but a route not affording 
thorough drainage should not be selected. 


6. Suitable Material for Roadway.—When there is any 
difference in the character of the soil along the different 
routes, the route having the best material should be selected 
as the best route, provided all other conditions are fulfilled 
to an equal extent. 


hy 


i. Small Cost.—With allof the above conditions equally 
fulfilled, the route which can be constructed and maintained 


STREETS AND HIGHWAYS. 1007 


at the least cost will be the best route to select. The mat- 
ter of cost is a very important consideration, and, in many 
cases, it will be the governing condition as against all other 
conditions. 

From the above, it will be noticed that the considerations 
involved in the comparison of the routes are of two kinds, 
namely, those relating to the efficient accommodation of the 
traffic, which is the result produced, and those relating to 
the cost of producing this result. The first six conditions 
named above are of the former class; the last condition only 
is of the latter class. In some cases, however, the last con- 
dition will outweigh all the others. 


1656. Means and Method of Comparison.—A 
comparison of all except the first of the conditions noticed 
in the preceding article will be given by the profiles of the 
routes. The length, grades, rise and fall, character of the 
soil, and, to some extent, the opportunity for thorough 
drainage, will be shown for each route by an inspection of 
its profile while the approximate cost of construction may 
be easily estimated from the same. 7 

In comparing the gradients, the rates of grade should 
be compared with special reference to the rates of maximum 
grade on the different routes, as this condition will greatly 
affect the magnitudes of the loads that can be hauled over 
the roads. 

In the comparison of the lengths of the routes, the total 
ineffective rise and the excessive fall should be included. By 
ineffective rise, as the term is here used, is meant that 
rise and fall in the grade line which is zo¢ due to the differ- 
ence of elevation between the two ends of the route; it is 
the total number of féet actual vzse in the grade line en- 
countered in passing from the higher end of the route #o the 
lower end. By excessive fall, as the term is here used, is 
meant that fall in the grade line which is in excess of cer- 
tain rates of grade encountered in passing in the same 
direction. Should the grade line on any portion of the 
route, in passing from the higher to the lower end, fai/ 


L008 STREETS AND HIGHWAYS. 


more than 9 per cent., 6.5 per-cent., or 3. percent tfor earin, 
gravel, or macadam roads, respectively, then each foot of 
fall zx excess of such rates will be considered as excessive 
fall. These are about the average rates of grade, giving, 
respectively, what is known as the angle of repose for the 
three kinds of roadways named; on descending grades 
steeper than these, a holding-back force must necessarily be 
applied to the loads. Ineffective rise and excessive fall are 
both counted in a direction passing from the higher to the 
lower end of the line.* 


1657. Comparison of Lengths.—The length of the 
route, taken in connection with the ineffective rise and ex- 
cessive fall, will here be called its resisting length. The 
resisting lengths of different routes may be compared by 
referring them to the work required to move a given load 
over them. If m is the coefficient of friction, the work zw 
performed in hauling a weight W along a horizontal dis- 
tancexhisw=Wmh. If, however, in the distance / there 
occurs a rise (or excessive fall) 7, the work necessary to haul 
the weight along the inclined path is w=Wmht Wr. 
In order to reduce this to an equivalent level grade we must 
give wa form similar-to that of.” €Puv then, 


r 7 
Whereis oa and the value of w' becomes w'’ = Wmh+ 
7 = 


Wim h'= Wm (h-+h'), which shows that the inclined path 
is equivalent to the corresponding horizontal path increased 


by the quantity 4%’, or. In general, if 7 is the length of a 


route, and /, the equivalent length of a route having, with 
respect to the former, asum of excessive falls and ineffective 
rises equal to 7, we have 


Lt Lae (203.) 


* Given a body resting on an inclined plane, the body will generally 
slide down the plane. But if the inclination of the plane to the horizon 
is gradually diminished, a limit will be reached at which the resistance 
of friction is just enough to prevent sliding. This inclination is called 
the angle of repose. It is different for different materials. The 
tangent of the angle of repose zs egual to the coefficient of friction. 


STREETS AND HIGHWAYS. 1009 


, and may have the following* values: 


: yi 
where ¢ is equal to — 
we 


For earth roads, Co Le 
For gravel roads, eee: 


ony 


For macdadam roads, ¢ = 33. 


By comparing the resisting lengths obtained by applying 
formula 203 to the grade lines of the different routes, a 
reasonably just comparison may be made between the 
routes with regard to what may be considered as their com- 
parative resistances to traffic by reason of actual length, 
ineffective rise, and excessive fall. 


1658. Soil, Traffic, Cost.—Some comparison of the 
character of the soils along the different routes, with ref- 
erence to their adaptability to the purposes of road build- 
ing, may be obtained from the notes given on the profile. 
For each route the opportunity for thorough drainage can 
be largely judged from the profile, enabling a reasonably 
just comparison of this condition also to be made. The 
amount of grading, as estimated for cach line from its pro- 
file, taken in connection with the amount of bridging and 
number of culverts required, as shown on the profile, will 
setve as a basis for estimating the relative cost of the 
different lines. 

A comparison of the first condition, convenience to traf- 
fic, can be made only from an examination of the routes on 
the ground or from a very complete map. The road should, 
so far as practicable, be so located as to be the most con- 
venient for the greatest portion of its traffic. The positicn 
of a road that will best accommodate its traffic will gener- 
ally be that in which, all other conditions being equal, the 
sum of the distances through which each ton of freight is 
moved and each passenger travels will be a minimum; in 
other words, it will be that position which will require the 


* These are about average values and may be used for ordinary 
roads. The actual values will generally vary from about 7 to 22 for 
earth roads, 15 to 80 for gravel roads, and 80 to 40 for macadam roads, 
according to the condition of the roadway surface. (Sec Art. 1647.) 


1010 STREETS AND HIGHWAYS. 










; 3 

: : 

Ss S 
3 
| 

Sl = 

= Nd 
8 
2 
wR 

250 
S| 






Mi mH i 
nt 
| iil 

ial 









Za 
— eon 
a SIE EEE es 























Fic. 399, 


STREETS AND HIGHWAYS. 1011 


mass of the traffic to be moved the least distance in reach- 
ing its destination. Some consideration should also be 
given to the question of whether a road will be pleasant for 
those who are to travel upon it. In the case of pleasure 
drives, this should be an important consideration. 

The basis of comparison with regard to economical loca- 
tion has been concisely stated by Prof. Spalding in the 
following language: ‘‘ The most cconomical location is that 
for which the sum of the annual costs of transportation, the 
annual costs for maintenance, and the interest on the cost 
of construction, is a minimum.”’ 


IX AMPLE OF ROAD LOCATION. 


1659. The Conditions Assumed.— Let it be assumed 
that it is desired to locate and construct a highway between 
the points A and #4, Fig. 399, which are 6,000 feet, or 
slightly more than 14 miles, apart, measured in a direct line. 
The topographical features of the country are quite clearly 
shown in the figure, the relative elevations being shown by 
contour lines. It will be assumed that the road is to be 
constructed to sustain a very heavy traffic between the 
points A and 4, and that it is not essential for it to pass 
through any intermediate points, though rather desirable 
that it should pass through or near the points @ and e in the 
valley, provided such location will not be disadvantageous 
in other respects. As the road is one of considerable im- 
portance, several routes are surveyed, in order to determine 
the best route. ‘The profiles of the difterent routes are 
shown below the map in Fig. 399. Only the surface lines 
are shown in these profiles. In order to avoid confusion in 
comparing the different profiles, the grade lines have been 
omitted; they may be considered to have approximately the 
same positions as the surface lines and to be somewhat more 
uniform. 


1660. The direct route Aadc Vis the shortest as 
regards hcrizontal distance, being just 6,000 feet long, hori- 
zontally. But the profile shows that, in passing from the 


1012 STREETS AND IIGHWAYS. 


higher terminus 1 to the lower terminus 4, by this route, 
a rise of about 43 feet is encountered between a and J, 
and another rise of about 19 feet occurs betweenc and 4, 
inaking a total ineffective rise on this route of 43-+19= 62 
feet. Between the end A of the line and the first crossing 
of the stream, which is a distance of 625 feet, the fall is 
vo X LOO 

Hesie 
suming that the road is to be an ordinary earth road, then, 
as stated in Art. 1649, that portion of the fall in excess 
of 9 per cent. should be treated as a like amount of rise. 
A fall of 9 per cent. for a distance of 625 feet would bea 
total fall of 9 x 6.25 = 56.25 feet, leaving an excess of 75 — 
56.25 = 18.75 feet. Alsoin the 400 feet of horizontal dis- 
tance, situated between points distant 350 and 750 feet, 
respectively, to the right of J, the fall is about 50 feet, or at 
a rate of ee ='12:5' ‘per cént. ; which isean /exceseacn 
12.5 — 9 = 3.5 per cent:, or.a total excess of 4.00 X 3.5 = 14 
feet. By applying formula 203; the length of route /, to 
be assumed in making the comparison will be equal to 
6,000 + 12 x (624+ 18.75 + 14) = 7,137 feet. This route 
would also involve very steep grades, the maximum in one 
direction being not less than 12 per cent., and in the opposite 
direction about 5 per cent. 


about 75 feet, or at the rate of =f 2 Der_COnte agri se 


1661. The route 4 dc J, following the general course 
of the stream, would usually be the route first tried, 
especially if the surveys were made from the lower terminus 
/ towards the upper terminus A, as will most commonly be 
the case. The surface line A de J’ is the profile of this 
route. It will be seen from this profile that the route is a quite 
favorable one, having only the very small amount of inef- 
fective rise that occurs betweenc’ and B. The length of this 
route is 6,250 feet. In the first 1,000 feet from A, however, 
this route has a fall of about 85 feet, requiring a grade of 
8.5 per cent., which is steeper than is desirable for the 
character of the traffic that the road is to sustain. . 


STREETS AND HIGHWAYS. 1013 


In the attempt to avoid this steep grade, the lines A 7’ s’d 
and A 7’ s' e are run as alternative lines for a portion of this 
route. The profiles of these lines are shown by the surface 
lines A?7’s’ ad and A?’ s' 2 respectively. The line A 7's’ d 
increases the length of the route by the amount dd’, or 
about 70) feet, and the line A 7’ s’ ¢ increases it by the amount 
ee, or about 600 feet. Hence, the total horizontal length 
of the line 4 s’d A will be 6,250 + 700 = 6,950 feet, and the 
total horizontal length of the line 4 s’ e & will be 6,250 + 
600 = 6,850 feet. There is no excessive fall in this line, but 
between the points c’ and & there is about 8 feet of ineffec- 
tive rise, giving a theoretical increase of 8 x 12 = 96 feet in 
the length of the line. For the purposes of comparison, 
therefore, the value /, for the line A s’d B is 6,950 + 96 = 
7,046 feet, and for the line 4 s’e B it is 6,850 + 96 = 6,946 
feet. For both these lines, the maximum grade is 5 per 
cent.; it occurs between 7’ and s’. 


1662. The route A fkmoB is surveyed at a higher 
elevation along the opposite side of the valley. This line is 
'amodification of the direct line Ad dc 4 ; it is quite crooked, 
however, and its length, horizontally, is about 7,060 feet. 
For this route, the surface line A #2 4" is the profile. Its 
maximum grade, which is between z and /, is 5 per cent. 
Between the point f and the terminus /, there is about 
12 feet of ineffective rise, making the value of Z, for this 


route equal to 7,060 + 12 x 12 = 7,204 feet. 


1663. The Route of Easiest Grade.-—As the traffic 
upon the road is to be of a very heavy character, making 
easy grades a very important consideration, still another 
line is surveyed, for the purpose of ascertaining whether a 
line having very easy grades can be obtained. This line is 
located very carefully, with the object of obtaining, if pos- 
sible, a line having no grade steeper than 2.5 per cent. Such 
a line is obtained; it isthe line 4 s ¢vw 4, having a length of 
about 7,550: feet. There is no ineffective rise or excessive 
fall on this line. The surface line A s¢w 4” is the profile 
of this line. The greater portion of the line approximates a 


1014 STREETS AND HIGHWAYS. 


uniform grade of 2.4 per cent., anda maximum grade of 2.5 
per cent. can be easily obtained. 


1664. The Tabulated Comparison.—lIn order to 
afford a ready comparison between the different lines sur- 
veyed, the values that have been determined are given below 
in tabularform. For convenience of reference, the different 
lines are numbered. 

This tabulation of values, together with the map and 
profiles of the routes will enable an intelligent selection of 
the route to be made. From the values of /,, and of the 
maximum grade, it is seen that routes number 2, number 4, 
and number 6 are the most favorable ones. Route number 2, 
or the direct route through the valley, is a thoroughly prac- 
tical route, provided the maximum grade of 8.5 per cent., 
extending for a distance of 1,000 feet, is not objectionable. 
This route gives the smallest value of 7. Route number 4 
is a modification of route number 2. It reduces the maxti- 
mum gerade to 6 per cent), and increases*the lenoth om ihe 
line nearly 700 feet. Route number 6 follows the brow of 
the hill on the left side of the valley. This is the longest 
of the routes surveyed, but it obtains the very easy maximum 
grade of 2.5 per cent., and, as it has no ineffective rise and 

















Actual Resisting | Maximum 
Number. Line. Lenvth 7 sic leosth 7a Grade, 
Feet. Feet. Per‘ Cent 
1 A peLb 6,000 mie t 12.0 
2 AdeBbB 6,250 6,250 8.5 
3 As'dB 6,950 7,046 5.0 
4 Arsseels 6,850 6,946 5.0 
5 Amob 7,060 7,204 3.0 
6 Aswh 7,550 7,550 RAD 








fall, it gives a value of 7, the same as the actual length of 
the line. This is much the best route for heavy traffic, and 


STREETS AND HIGHWAYS. 1015 


for a mixed traffic will generally be the most satisfactory. 
If the character of the traffic is light, so that a grade of 8.5 
per cent. is not a serious disadvantage, route number 2, 
leading directly through the valley, will generally be the 
most satisfactory. If it is necessary to pass through the 
points d and ¢, and, at the same time, have no grade steeper 
than 5 per cent., route number 3 will fulfil the conditions; 
but, if there is no reason why the road should pass through 
the point d, route number 4 will be slightly shorter. 


RELOCATION OF ROADS. 


1665. The Present Conditions.—In most parts of 
this country, so many roads are already located that the 
necessity for locating new ones does not often arise, and 
when such necessity does arise, the road is usually a short 
one and its position is determined mainly by the existing 
roads and local requirements. The problem that now most 
frequently occurs in the location of country roads is that of 
changing the location of short portions of existing roads, in 
order to obtain better grades, shorter routes, or better 
ground and drainage. 


1666. The Common Defects.—Heavy and unneces- 
sary grades are the most common defects of ordinary 
country roads. Such grades are often due to improper loca- 
tion. Many roads have been located along property lines 
and on the shortest obtainable routes, without due regard 
to the question of easy grades, even if the latter were easily 
obtainable. In such cases, the defect can be remedied by 
relocating all or a portionof the line. Sometimes, however, 
the road, as originally located, 1s unnecessarily long and 
devious, and it becomes necessary to relocate all ora portion 
of the road, in order to obtain a shorter and more direct 
route. Again, the character of the ground over which the 
road passes may be such that to maintain the road in good 
condition is difficult and expensive, and in some cases 
impossible. Better ground can generally be obtained by a 
new location. 


1016 STREETS AND HIGHWAYS. 


1667. Roads on Section Lines.—Almost all regions 
of the United States in which the Government lands have 
been surveyed since 1785 have been surveyed according to 
the system of rectangular townships and sections. In such 
portions of the country, it is a very common practice to 
locate the roads along section or quarter-section lines, and 
this practice has been the cause of a considerable amount of 
unfortunate road location. Where land boundaries are 
formed by section or quarter-section lines, as is commonly 
the case, the roads should preferably be located along such 
lines, provided such location is not in other respects disad- 
vantageous to the roads. Straight lines should not be 
followed, however, when more advantageous routes can be 
obtained. 


1668. The Example.—In Fig. 399 the straight route 
Abc B may represent an existing road constructed along a 
section line. This route proving quite unsatisfactory on 
account of its steep gradients, a new location is made on the 
line A gmo 4, having much easier grades. Again, the route 
Ade may represent an existing road following the general 
course of the stream through the valley. This road being 
satisfactory except as regards the 8.5 per cent. grade on that 
portion adjacent to the upper end A, a sufficient portion of 
this end of the road is relocated to obtain an easier grade. The 
location A 7’ s' d will be quite satisfactory for this purpose, 
except that it will require the abandonment of the entire 
portion A d of the old line, and the construction of about 
3,000 feet of new line. The location A 7’ s’ ad’ will retain 
all of the old line except the portion A-@”, or about 1.190 
feet, and will require the construction of only 2,000 feet of 
new line. The length of the line will be increased 2,000 — 
1,190 = 810 feet, by the relocation) OfSthis portico 
shown by the profile, the maximum grade on the relocated 
portion of the line will be about 5 per cent. 


1669. Maps and Records.—When the route of a 
highway has been satisfactorily and finally located, a map 
of the line should be made for the purpose of record, show- 


STREETS AND HIGHWAYS. 101% 


ing accurately all its courses, angles, and distances, the 
points at which it crosses land boundaries, section lines, 
streams, railroads, and existing highways, together with the 
courses and distances to, and the descriptions of, all wit- 
nesses taken at the angles and at the starting and terminal 
points of the line. The map should also show the positions 
of the starting and terminal points, and convenient points 
along the line, with reference to the nearest corners of the 
Government land survey. 

The map may also show a profile of the line, though, for 
a country road, this is not very essential, as the profile will 
not be of great value as a matter of record after the road is 
constructed. As a means of reference in regard to the 
grades and drainage, however, the profile will be convenient 
and should generally be shown. All inrormation given on 
the map proper, that is, all information relating to the 
alinement and position of the line, should also be given 
in an accurate written description of the surveyed line. 
The map and description should be filed with the proper 
township or county officials for a permanent record. 


MATTERS FOR PRACTICAL CONSIDERATION. 


WIDTH AND CROSS-SECTION. 

1670. Width of Right of Way.—The entire area of 
a road included between fence lines is known as the right 
of way; it is so called because it is the right of way for the 
road, which must be obtained, by purchase or otherwise, 
from the owners of the properties over which the road 
passes. The best width for the right of way of a road isa 
matter that must be determined by judgment and accord- 
ing to the requirements of each particular case. The 
widths of country roads vary greatly. A width of 4 rods, 
or 66 feet, is common for important roads in some parts of 
the country. In other parts of the country, very narrow 
roads are often met with, some being little more than nar- 
row lanes, probably not more than a rod in width. Roads 
3 rods, or 494 feet in width, are quite common. 

T. IV.—t4 


1018 STREETS AND HIGHWAYS. 


A width of 66 feet was probably first adopted largely for 
convenience of measurement and computation, it being the 
length of a surveyor’schain. It has proved to be a good 
practical width, however, and is not only used for many 
country roads but for city streets also. It is wide enough 
to accommodate all possible requirements, and is about as 
narrow, as is generally desirable for northern climates, for 
the snowdrifts caused by the fence lines often extend across 
and block the roadway in narrower roads. Rights of way 
narrower than 66 feet are, however, very common. 


1671. Width of Roadway.—The width of the graded 
driveway should be from 12 to 30 feet, according to the re- 
quirements of the travel. A width of 12 feet is ample for 
two teams to pass and is sufficient for cross roads and unim- 
portant roads in the country. A driveway 16 feet in width 
will often be sufficient for country highways that are main 
arteries of travel. The conditions requiring a width of 
30 feet for a roadway in the country are exceptional, and 
the conditions requiring greater widths are very rare. 

The width of the roadway should, in all cases, be limited 
to the requirements of the travel. It has been found that a 
width of roadway just sufficient to accommodate the travel 
is more enduring than a greater width. Any additional 
width beyond that necessary to accommodate the travel is 
almost always a disadvantage, for it lessens the possibility 
of effective drainage and otherwise impairs the condition of 
the roadway. 





1672. Cross-Section of Roadway.—Water is the 
chief enemy of good roads. In order that the water shall 
run off from the surface of the roadway, instead of soak- 
ing into it, the roadway should be crowned, that is, it 
should be made higher in the center than at the sides. 
The surface line should be given the form, in cross-section, 
of either the arc of a circle, or of two straight lines slop- 
ing downwards and outwards, with their two inner ends 
joined by the arc of a circle about five feet in length. 

The amount of crown, that is, the height of the center 


STREETS AND HIGHWAYS. 1019 


of the roadway above its edges, should be sufficient to 
effectively drain off the water from the roadway, but 
should not be great enough to cause inconvenience to the 
travel; it will generally be about one-fortieth of the width 
for ordinary earth roads,\about. one-sixtieth of the width 
for good macadam roads, and about one-eightieth of the 
width for well-paved streets. These ratios should be varied 
according to the character and condition of the roadway; 
a well-made roadway will require less crown than an in- 
ferior one. The reason for this will be readily understood 
when it is considered that the crown of the roadway is for 
the sole purpose of throwing off the water into the gutters 
or side drains. 


DRAINAGE AND WATERWAYS. 


1673. Drainage.—All matters relating to the loca- 
tion and construction of a highway should conform to, and 
be directed towards, a condition of thorough drainage. 
The alinement should be such as to give proper grades, 
and the grades should, in turn, be such as to give effectual 
drainage. For thorough drainage is the condition most 
essential to a good road. A vast amount of water falls 
upon a mile of roadway during a year. If the roadway is 
to remain in good condition, it is imperatively necessary 
that escape be provided for this water in some other man- 
ner than by soaking into the roadway or into the ground 
at the sides of the roadway. Ground saturated with water 
can form neither a good roadway nor a good foundation for 
a roadway. On the other hand, some materials which when 
water soaked are thoroughly unreliable will, when effectually 
drained, become reasonably satisfactory for the purposes of 
a roadway. For instance, a roadbed of either clay or quick- 
sand wouid, if completely water soaked, be almost, if not 
quite, impassable. Buta mixture of clay and quicksand, 
if kept thoroughly drained, would make a: reasonably good 
road. 

The water should be promptly removed by means of sur- 
face ditches along or near the edges of the roadway. As 


1020 STREETS AND HIGHWAYS. 


some of the water will always soak into the ground, even 
with the most perfect system of surface drainage, drains 
should also be placed beneath the roadway to effectually 
remove the water from the subsoil. Such drains will here- 
be called subsoil drains. Where the ground is naturally 
dry, or where the earth foundation of the roadway is com- 
posed of a material not rendered soft and yielding by water, 
the subsoil drains may be omitted and the drainage effected 
entirely by the side ditches. 


1674. Arrangement of Drains.—Fig. 400 repre- 
sents the cross-section of a roadway; it is not drawn to 
scale, and is intended merely to show the general arrange- 
ment of the drainage system. The material of which this 





Fic. 400. 


roadway is composed is not indicated, as the principles of 
drainage will apply much the same for any material. By 
reason of the crown given to the roadway 7, the greater 
portion of the storm water will be thrown off into the side 
ditches @ and a’, along which it will flow to some outlet 
into a natural drainage channel. In the figure, the outlet 
to the side ditches is shown at o; the ditches discharge a 
this point by means of the cross drain 6, which may reprc- 
sent any drain leading from the side ditches to the outlet. 
The arrangement of the outlet drain here shown is not 
necessarily the best for this purpose; it is simply an arrange- 
ment suited to the conditions shown. The side ditches may 
often discharge directly into a stream or a larger ditch 
crossing the roadway. 

The subsoil drains d@ and ad’ are placed beneath the road- 
way for the purpose of rendering the drainage complete and 
effectual by removing the water from the subsoil, That 


STREETS AND HIGHWAYS. 1021 


portion of the cross-section drained by the subsoil drains is 
shown by lighter shading than the undrained portion below. 
The drain d@ is represented as an ordinary small tile drain, 
and the drain @'is represented asa common stonedrain. In 
an actual case, both drains would generally be of the same 
kind; the two kinds are here shown merely for illustration. 
Stone drains are formed by simply filling a narrow trench 
with stones, the larger stones being placed at the bottom 
and the smaller ones towards the top. The trenches 
in which tile drains are laid are often filled with gravel 
and small ‘stones for a considerable distance above the 
drains. 

The subsoil drains shown in Fig. 400 discharge by means 
of the cross drain ¢ leading to the outlet o’. This cross 
drain need not be as large as the cross drain 6 which con- 
veys the storm water from the side ditches. The arrange- 
ment for conveying the water from the side ditches and 
subsoil drains to the channels of natural drainage should, 
of course, be varied to suit the requirements of each 
particular case. When cross drains are employed, they will 
not usually be in the same vertical cross-section, as shown 
here for convenience. 


1675. Single Subsoil Drains.—It is cheaper to use 
a single drain, placing it under the center, than to use two 





Fic. 401, 


drains under the edges of the roadway. Single drains are 
the more commonly used. The cross-section of an ordinary 
earth road having shallow side ditches and a single subsoil 
drain is shown in Fig. 401. The drain here shown is made 
of flat stones laid up in box form, and covered with a layer 
of small stones. Where flat stones are abundant, this is a 


1022 STREETS AND HIGHWAYS. 


cheap form of drain. The layer of small stones is often 
omitted. Tile drains and ordinary stone drains are also 
used; tile drains are best for the purpose. 

Good drainage may generally be obtained by single sub- 
soil drains, but any examination or repairs of such drains 
will necessitate the disturbance of the roadway, which is un- 
desirable. By placing the subsoil drains under the outer 
edges of the roadway, they can be inspected and repaired 
whenever necessary, without disturbing the central and 
most important portion of the roadway. ‘Two drains under 
the outer edges will also give more efficient drainage than a 
single drain. 


1676. Dimensions, Depth, and Alinement of 
Drains.—The diameters of the tiles used for subsoil drains 
should be between 3 and 5inches. Subsoil drains should 
be placed at sufficient depth below the surface to escape the 
destructive action of frost. The depth necessary to escape 
frost will vary in different localities; a depth of 34 feet may 
be taken as a safe average. 

The side ditches should be given such depth as to prompt- 
ly and effectually remove the surface water. Where subsoil 
drains are not used, the side ditches should have sufficient 
depths to drain the subsoil also. The best depth will, in any 
case, depend upon the nature of the soil, the natural drain- 
age, and the position of the outlet. The slopes of the sides 
of the ditches should not be steeper than 1 vertical to 1 hor- 
izontal, and, in very unstable soils, not steeper than 1 ver- 
tical to 14 horizontal. 

The side ditches and subsoil drains should be constructed 
upon either straight lines or uniform curves, and to uniform 
grades. This is very important in order to develop any- 
thing like the full carrying capacity of the drains and 
ditches, for the flow of the water is greatly retarded by 
crooks and irregularities in the channel. The tile drains, 
especially, are very liable to become choked by the deposits 
of solid matter caused by the retardation of the current, due 
to irregularities of grade and alinement, although, for- 


STREETS AND HIGHWAYS. 1023 


tunately, subsoil drains carry comparatively little solid 
matter in suspension. 


1677. Necessity for Waterways.—Ditches and 
drains are provided along and beneath a roadway for the 
purpose of draining it. In order to convey the drainage 
water from the ditches on the upper side of the roadway to 
a suitable outlet, it is generally necessary to provide means 
for it to cross the roadway. Provision must also be made 
for the drainage waters from adjacent lands to cross the 
roadway. «This drainage water may flow in natural chan- 
nels, as in the case of brooks and rivers, or in artificial 
channels, as in the case of ditches and drains. Wherever a 
stream of water crosses the road, an opening through or be- 
neath the roadway must be made for it, whatever may be 
the size of the stream or the kind of channel. 


1678. Required Size of Waterways.—The re- 
quired size of the waterways is the first thing to be deter- 
mined in deciding upon the character of the opening. The 
waterway provided must be large enough to pass the maxi- 
mum flow of water that is likely to be given by the stream, 
while considerations of economy require that it shall not be 
larger than this. Hence, the size of waterway required by 
the maximum flow of the stream is what it is necessary to 
determine as nearly as possible. 

The maximum flow of a stream will depend upon a num- 
ber of conditions, the most prominent of which are the 
maximum rate of rainfall; the size, shape, character of sur- 
face, and slope of the area drained; and the length, position, 
character, and slope of the channel. Most of these con- 
ditions are of difficult accurate determination, and can not 
be expressed by exact mathematical formulas. It will be 
noticed, however, that the conditions are analogous to those 
for determining the required size of a storm-water sewer, as 
studied in the section on Drainage. The maximum storm 
effluent from the area drained by the stream may be found 
by the method there given, and the required size of the 
opening may be found by treating it as a pipe flowing full 


1024. STREETS AND HIGHWAYS. 


if it is a closed culvert, or as an open channel if it is anopen 
culvert or bridge. 

It is generally advisable, however, to measure the flow of 
the stream at high water, if opportunity is afforded for doing 
so. An idea of what size of opening may be required for 
the maximum flow can generally be acquired more accurate- 
ly by this than by any other method. In many cases, some 
person living in-the vicinity will be able to point out the 
highest point reached by the water, from which information 
the size required for the waterway can be easily determined. 


1679. Formula for Waterway.—When not prac- 
ticable to measure the flow of the stream at high water, the - 
required capacity of the waterway may be estimated with 
sufficient accuracy by applying the following formula : 


We EAE, (204.) 


in which a is the required area of the opening in square feet, 
A is the drainage area in acres, and ¢ isa coefficient depend- 
ing upon the nature of the country and of the channel of the 
stream. The following values are used forc: 


For comparatively level areas, c = 1.0. 
For compact, hilly ground, ae ee 
For abrupt, rocky slopes, eget AAUP 


For conditions intermediate between those described, in- 
termediate values of ¢ may be used. 

The value of c should be somewhat higher for an approxi- 
mately square area than for a long, narrow valley, and higher 
for soil of an impervious nature than for porous soil. If the 
course of the stream is reasonably straight, or if it has con-’ 
siderable fall and rapid current, the value of c should be 
greater thanif the stream has a winding and tortuous course, 
or very little fall and a sluggish current. If judgment and 
care are exercised in the use of the coefficient, reasonably 
good results may be obtained with this formula, and it has 
the advantage of great simplicity. 

It will be well to notice that a more rational expression 
for the required area of the waterway would appear to in- 


STREETS AND HIGHWAYS. 1025 


volve the fourth root of the third power of A, similar to the 
Buerkli formula for storm-water effluent. (See formula 
118, Art. 1451.) Such a formula for waterways has been 
proposed. As, however, the accuracy of this formula, and 
of any similar formula that can be proposed, will depend 
very largely upon the use of a suitable value for the co- 
efficient, and as a considerable margin of safety must be 
allowed in the area of a waterway, as determined by any 
formula, it is believed that the one stated above will be found 
about as satisfactory as any. 

EXAMPLE.—What size of waterway is required for a stream draining 
400 acres of hilly ground, the soil being of a quite compact nature ? 

SOLUTION.—For such a drainage area, the value of c will be 1.6; 
hence, by applying formula 204, the required area of the waterway is 
found to be 1.6 4/400 = 32 square feet. A waterway 4x8 feet will 
give the required area. 





MATTERS RELATING TO THE CONSTRUCTION 
OF HIGHWAYS. 


ROADS AND MATERIALS. 
1680. Materials Available for Country Roads.— 
The roads which can be constructed from the materials and 
with the means ordinarily available in the country may be 





classified as broken stone roads, gravel roads, and 
earth roads. More costly roads are not at present neces- 
sary in the country, and could not be constructed with the 
means available. Indeed, in many places, lack of means 
prevents the construction of any but the last-named class of 
roads. 

BROKEN STONE ROADS. 

1681. Of What They Consist.—A broken stone road 
consists essentially of a layer, or wearing surface, composed 
of fragments of broken rock, spread upon a foundation pre- 
pared toreceive it, the whole being consolidated to a firm, 
uniform surface by rolling or by the traffic passing over it. 
The fragments of broken rock so used are sometimes called 
road-metal. Roads constructed of broken stone are classi- 
fied as macadam roads and telford roads, from the 





1026 STREETS AND HIGHWAYS. 


names of their originators. The appearance of the comple- 
ted roadway is practically the same in both systems, the 
distinguishing features being in the foundations. 
Macadam’s system consists essentiaily in spreading and 
compacting one or more uniform layers of suitable rock 
broken into cubes of nearly uniform size directly upon an 
earth foundation which has been previously formed to the 
proper grade and cross-section and thoroughly compacted by 
rolling. A cross-section of a macadam road is shown in Fig. 
402. Telford’s system is much the same as Macadam’s 





PITH TTI VAT OE 
iauisanssistartebatrepaeee 





Soo 

a (ibeanawsee, 
ILD 4 
wamraasern’ 









ay 


Ue 


WW 


MSS 


L\\ 


FIG. 402. 


except that the layer of broken stone forming the wearing 
surface is spread upon a paved foundation. This paved 
foundation is formed by blocks of stone from 3 to 8 inches in 
depth, set close together upon their broadest edges. The 
_ cross-section of a tel- 
} ford roadway is shown 
| in Fig. 403. The blocks 
‘ .4 of stone are set upon the 
SS earth foundation and 
their sizes graduated according to their position, as shown 
in the figure. 

Macadam’s system is the more popular in this country. 
When properly constructed, it has been found to makea 
satisfactory roadway, and is considerably cheaper than 
Telford’s system. The expense of the latter system is too 
great for it to be available for ordinary country roads. 
All broken stone roads referred to in this course will be 
understood to be macadam roads. 

For those important suburban roads on which the travel 
is ofa character not requiring a more substantial pavement, 
and for those country roads on which the travel is of sufficient 
importance to warrant the outlay, broken stone may be very 
advantageously used as a road material. It is doubtful, 
however, whether this material will ever be very generally 






ISHN 


STREETS AND HIGHWAYS. 1027 


used for country roads, asthe expense of construction and 
maintenance would, in many cases, be greater than the im- 
portance of the road would warrant. The cost of construct- 
ing macadam roads will generally be from about two to five 
thousand dollars per mile, a cost which, for most country 
roads, is prohibitory. 





1682. Quality of the Broken Stone.—A _ good 
quality of stone should be selected for road material. The 
stone should be hard, tough, and elastic, and should have good 
binding properties. It should offer ahigh degree of resist- 
ance to abrasion, but need not necessarily be of high crush- 
ing strength. The stone should also be of such quality as 
not to soften or deteriorate under the action of the atmos- 
phere. ‘Toughness and resistance to abrasion are two very 
essential qualities. 

The varieties of rock most suitable for road-metal are ¢ra/, 
syentte, granite, chert, limestone, mica-schist, and quarts. 
These are named in the order of theirrelative values. Sand- 
stone, clayey slate, and rock of indurated clayey material 
are not suitable for road-metal. Sandstone is not suitable 
because it, has practically no binding properties; the frag- 
ments do not bind together to forma solid mass, but remain 
simply an accumulation of separate fragments, which soon 
become ground and crushed into sand by the traffic. Clayey 
stones have poor binding qualities, and, when saturated with 
water, become very soft and easily crush into mud. 


1683. Size of Broken Stone.—Before being spread 
upon the roadway, the stone should be broken into small 
fragments. The proper size for these will depend, to some 
extent, upon the nature of the material. The harder and 
tougher the material, the smaller the fragments should gen- 
erally be. A common rule requires that the stone shall be 
broken small enough to pass through a 24-inch ring. It is 
also a not uncommon practice to use somewhat larger pieces 
in the bottom courses of the roadway than at the top, the 
stones at the bottom being from 2 to 3 inches in greatest 
dimension and those at the surface not more than 2 inches. 


1028 STREETS: AN DeHIGAW yo. 


This is probably a good practice, though it may be doubt- 
ful whether it is sufficiently advantageous to warrant the 
additional expense of separating the sizes. Opinions differ 
as to the best practice. Some advocate the use of stone of 
uniform size, while others believe that the best results are 
obtained by using sizes varying from a maximum of about 
2 inches down toa minimum ‘of about 2? of an inch. The | 
fact is, probably, that stone of uniform size will wear more 
evenly, while variable sizes and the presence of smaller 


ae, 
fragments facilitate the binding together of the mass. 


GRAVEL ROADS. 
1684. Where Adaptable.—Where gravel of suitable 
quality can be obtained in the vicinity, it will generally be 
the best available material for an ordinary country road. 
This will be especially the case for roads on which the char- 
acter of the trafficis hght. Where suitable gravel is obtain- 
able, the cost of a well-constructed gravel roadway will 
generally be not more than from one-quarter to one-half 
that of an equally well constructed macadam roadway. In 
order to be maintained in equally good condition, however, 
the gravel roadway will require more attention: and more 
frequent repairs than the macadam roadway. But it should 
be understood that, for ordinary travel of a rather light 
character, it is quite possible to maintain a properly con- 
structed gravel road in a condition equal to that of a 
macadam road. The cost of such maintenance, however, 
would probably be about one and one-half times that of the 
macadam road. | 
The subject of gravel roads, and of gravel as a road 
material, is of great importance in this country, and is 
deserving of closer attention than it has received. Although 
gravel is a popular material for road making in the country, 
because it is well known to be the best natural material 
available, yet its possibilities as a road material are not well 
understood. For light travel, a gravel road, properly con- 
structed and maintained, with thorough drainage, may be 
an ideal road. 


STREETS AND HIGHWAYS. 1029 


1685. Quality of the Gravel.—Gravel consists of | 
small fragments of stone, broken from the original bed-rock 
and more or less rounded by the action of water and ice, 
the pebbles thus formed generally representing the most en- 
during portions of the original rock. The varieties of gravel 
are many and diverse, and the quality varies exceedingly, 
according to the nature of the original rock, the action of 
the water, and the extent that the material is affected by 
decay. On this account it is difficult to make any very 
definite statements concerning the different varieties of 
gravel. ; 

Among the best gravels for road purposes in this country 
are those known in New England as blue gravels. They 
consist of fragments of undecayed rock of a trappean nature, 
and occur in considerable quantities in the northeastern 
portion of Massachusetts. Gravel composed mainly of white 
quartz pebbles is of very little value as a road material. 
These pebbles are very smooth and possess scarcely any 
binding power; where they constitute more than half the 
mass, the gravel is usually worthless as a covering material 
for roads, unless mixed with some binding material.  Be- 
tween these two extremes, that is, between the undecayed 
trap pebbles, which are the best, and the white quartz 
pebbles, which have the least value, are the pebbles of 
syenite, granite, chert, limestone, and mica-schist, occurring 


> 
in great variety and widely differing quality, but all pos- 
sessing more or less value as road material. Much the 


same qualities are desirable for gravel as a road material as 
those that have been noticed for broken stone. 

The gravel for road material should be sharp and com- 
paratively clean; it should be screened before being spread 
upon the roadway, in order to separate from it the excess- 
ively large pebbles and also the injuriously fine and loamy 
material. If found mingled with a large proportion of clay, 
it will be worth while to wash it. Gravel for road material 
should not contain more than one-fourth part sand or clay, 
and not more than one-half of its pebbles should be com- 
posed of white quartz. Gravel composed of stones of 


1030 STREETS AND HIGHWAYS. 


angular form, such as is taken from pits, is much better for 
road purposes than that composed of round or oval pebbles, 
such as is commonly found in the beds of streams. 

Where the gravel is composed largely of white quartz, 
round smooth pebbles, or any material having small cement- 
ing capacity, a binding material should be added. Probably 
the best available material for this purpose is the ordinary 
red or brown iron ore found in nearly ail parts of the 
country. It is very common in swamps, and is valuable for 
this purpose even when very impure. Where this ore is not 
available, a small admixture of clay will serve as a fairly 
good substitute. 


EARTH ROADS. 

1686. The Conditions.—In many cases, gravel for 
road material is not obtainable, and the cost of broken stone 
is so great that the importance of the road will not warrant 
its.use. In stich cases, the road must be sngde ofssiien 
material as is available, and this material should be so used 
as to give the best possible results. Where the travel is not 
of too heavy a character, a quite satisfactory road can be 
maintained with ordinary earth material, provided the 
drainage is thorough. 

It is well to notice that comparatively few of the earth 
roads throughout the country are as good as they could 
easily be made to be. By reason, largely,of improper location, 
insufficient drainage, and neglect, the average country road 
is in a condition far from satisfactory during a large portion 
of each year. By changing the location, where necessary, 
and by thorough drainage and prompt and systematic re- 
pairs, the condition of country roads may be greatly im- 
proved without much additional expenditure. 


1687. Materials of Earth Roads.—A thoroughly 
drained clay road may be quite satisfactory for ordinary 
travel; even a road constructed of quicksand, if very thor- 
oughly drained, may sustain light travel fairly well. For 
such roads, however, thorough drainage of both the surface 
and subsoil is absolutely essential, and the fact can not be 


STREETS AND HIGHWAYS. 1031 


too strongly emphasized. Clay roads will not generally 
become so dusty in dry weather as to be unpleasant for 
travel; but, if not thoroughly drained, they may become 
nearly or quite impassable in wet weather. Quicksand, 
when thoroughly saturated with water, will not only be im- 
passable, but also dangerous. 

Clean, silicious sand is, of itself, a very poor road material. 
It has scarcely any binding power and will not pack so as to 
give a firm, unyielding surface. The value of such sand 
may be much increased by mixing with it a certain propor- 
tion of clay as a binding material. A mixture of sand and 
clay in proper proportions makes a good road material, and 
the addition of clay to a sand road, or the addition of sand 
to a clay road, will generally much improve either. The 
material known as hardpan, which is a general mixture of 
clay and gravel, is an excellent material for roads. When 
it contains too large a proportion of clay, clean gravel or 
sand should be added. 

Loam, containing a large proportion of decomposed vege- 
table matter, is about the least valuable of the materials 
employed for road-making purposes. Loam is composed 
chiefly of silicious sand, clay, carbonate of lime, and vegetable 
mold, orhumus. The character of loam varies greatly, ac- 
cording to the proportions of its different ingredients; its 
value as a road material will be about in proportion to its 
freedom from decomposing vegetable matter. 


ROAD CONSTRUCTION, 


BROKEN STONE AND GRAVEL ROADS; DRAINAGE AND 
FOUNDATION. 


1688. Drainage System. — The system of drains 
should generally be constructed first. Where cuttings occur, 
however, such cuttings as are necessary to form the road- 
way must be made before the drains are constructed. The 
ditches and drains should be laid out with care. The 
arrangement of the drainage system has been noticed quite 


fully in Art. 1674. The best positions for the side ditches 


1032 STREETS AND HIGHWAYS: 


and subsoil drains will depend principally upon the charac- 
ter of the soil and the covering material used for the road- 
way, and also, to some extent, upon the topography of the 
country. Systematic subsoil drainage will generally be 
necessary in localities where there is a lack of natural drain- 
age. . In some cases, however, the subsoil may be quite 
effectually drained by deep side ditches placed a few feet 
outside of the outer edges of the roadway. 


1689. Preparing the Foundation. — For gravel 
and macadam roads, the earth foundation of the roadway, 
which is sometimes called the roadbed, should be formed 
to the proper grade and cross-section, and thoroughly com- 
pacted by rolling, before putting on the covering or surface 
material. The surface line of this earth foundation, which 
is called the subgrade, should be, when the foundation is 
finished, at a distance below the grade line equal to the in- 
tended thickness of the covering material. The earth 
foundation should slope from the center each way towards 
the gutter. , This slope’should: asa rule: beat the sates 
about 1 in 30; that is, the roadway should be given a crown 
equal to about one-sixtieth of its width, but this crown 
should be in the form of two uniform slopes falling outwards 
and connected at the center by a short curve, rather than 
wholly in the form of a curve. 

Where the surface of the completed roadway, for a gravel 
or macadam road, is not materially higher than the 





Y Yy 7 V7 7 M0 . 


Fia. 404. 


natural surface of the ground, the roadbed is formed by 
excavating a shallow trench of the proper width to receive 
the covering material. This is clearly shown in Fig. 404, 
which is the cross-section of a macadam road for which the 
drainage is effected wholly by the deep side ditches d@ and a. 
In some cases, flat stones or planks are set on edge along the 


STREETS AND HIGHWAYS: 1033 


outer edges of the roadway, as at c and c’, forming what is 
called curbing, but this is not usual for country roads. In 
the figure s is the subgrade; it is at the surface of the road- 
way foundation. 

In preparing the foundation, the excavation should be 
made to sufficient depth to remove the surface soil and all 
material containing vegetable mold, roots, and decaying 
matter of any kind. The excavation should, where practic- 
able, be carried downwards until a satisfactory material, 
such as firm gravel, compact sand, or true hardpan is reached. 
If a consolidated undersoil or hardpan is encountered a short 
distance below the surface, this should not be broken, even 
if is somewhat above subgrade, as it will afford a better 
foundation than can be obtained at greater depth. A clay 
foundation should be thoroughly underdrained. If the ex- 
cavation extends below subgrade, it should be brought up to 
subgrade by filling in suitable material, such as gravel, sand, 
a mixture of sand and clay, etc. The foundation should 
then be thoroughly compacted by rolling with a heavy 
roller. After a thorough rolling, the surface will be more 
or less uneven. The irregularities in the surface must be 
removed by cutting down the high places and filling in the 
hollows, after which the rolling is continued. This process 
is continued until a firm and even surface is obtained. 
Upon the foundation thus prepared, the covering material 
is spread, 


CONSTRUCTING THE ROADWAY. 


1690. Applying the Surface Material; Broken 
Stone.—lIf the covering material is broken stone, it should 
be applied in layers not exceeding 5 inches in thickness, and 
each layer thoroughly rolled. As the rolling continues, the 
hollows formed should be filled with material of small size, 
so that the surface will be even. On the last layer, the roll- 
ing should be continued until the material is so compacted 
that the rolling produces no perceptible motion. The stones 
will then be bound together in a compact mass. ‘This bind- 
ing together of the stones is due chiefly to the fine particles 


T. IV.—41o 


1034 STREETS AND HIGHWAYS. 


and small fragments of stone which are ground and crushed 
from the larger pieces by the process of rolling. These fine 
particles form a mortar or cement, which fills the interstices 
between the stones near the surface and binds them together. 
This will be especially the case with limestone. When the 
binding process is thorough, it forms a continuous crust 
with a hard, smooth surface, which has the appearance of a 
solid mass and is almost impervious to water. The com- 
pacting and binding may be assisted by watering moderately 
during the process of rolling. Water in large quantities, 
however, would have the opposite effect. The stone dust, 
or fine fragments of stone formed by the stone-crusher in 
the process of crushing, if spread upon the surface of the 
broken stone covering before or during the process of roll- 
ing, will aid the binding. 

The necessary thickness of the covering of broken stone 
will depend upon the nature of the foundation, the thorough- 
ness of the drainage, the completeness of the binding, and 
the character of the traffic to be sustained. Less thickness 
will be required by light travel than by heavy travel; a 
covering well bound together need not be as thick as an 
imperfectly bound covering; a firm, thoroughly drained 
foundation will not require as thick a covering asa less perfect 
foundation. The thickness of the covering of broken stone 
should not be less than 4 inches, and a thickness greater than 
12 inches will seldom be required. Macadam considered 
10 inches of well-compacted broken stone upon a solid, well- 
drained earth foundation sufficient for a roadway sustain- 
ing the heaviest traffic. A thickness of from 8 to 10 inches 
is sufficient in almost all cases. 


1691. Construction of Gravel Roadways.—Gravel 
roads should be constructed in the same general manner as 
macadam roads, although they may be constructed on a 
more liberal basis, and the principles of construction need 
not be so rigidly adhered to. The conditions relating to the 
preparation of the foundation, thickness of the covering 
material, and thorough compacting should be substantially 


STREETS AND HIGHWAYS. 1039 


as described above for broken stone roads, although the 
gravel covering may, with advantage, be made thicker than 
is necessary for broken stone, and the question of economy 
is not generally of so great importance. The addition of 
gravel to an earth road, under almost any circumstances, 
can scarcely fail to be an improvement. 

In certain cases, even a light layer of gravel may prove a 
great benefit. Where the subsoil is of a porous nature and 
. well drained, a light layer of gravel, well compacted, will 
effect a very material improvement. Where the material 
of the roadbed is clay, however, the thickness of the layer 
of gravel should be not less than 6 inches, and should pref- 
erably be more. In general, the thickness of the covering 
of gravel should be from 4 to 12 inches, and even a greater 
thickness will almost always be beneficial. It is advanta- 
geous to thoroughly compact both the earth foundation and 
the gravel covering by rolling. A smooth, firm surface 
may thus be produced which will be but little affected by 
the wheels of vehicles. If the rolling is omitted and the 
compacting left to vehicles, the gravel covering should be 
quite sharply crowned, as the tendency of the traffic will be 
to flatten it. 


EARTH ROADS. 

1692. Construction of Earth Roadways; Drain- 
age.—In the construction of earth roads, the most essential 
conditions are ordinarily thorough drainage for both the 
surface and subsoil, and thorough compacting of the road- 
way surface. Thisis especially the case with roads of clayey 
material. Roadways of nearly pure sand, however, are 
injured rather than benefited by thorough drainage, as the 
sand is more firm and stable-in a damp condition than when 
dry. Roadways in light soil of a sandy nature, having a 
good natural drainage, will seldom require artificial drainage. 


1693. Proper Use of Materials.—In the prepara- 
tion of the roadway, all material containing roots and 
vegetable matter should be removed; if this necessitates 
excavating below the intended surface of the finished 


1036 STREETS AND HIGHWAYS. 


roadway, the excavation should be refilled with the best 
material obtainable. Judgment should be exercised in the 
selection of this filling material. It should be of such char- 
acter as to improve the condition of the natural foundation 
when mingled with it. 

A judicious mixture of sand and clay will make a better 
road than either material by itself. When clean, coarse 
sand or gravel is mixed with just sufficient clay to bind the 
particles together, a very hard and compact mass is formed . 
that is nearly impervious to water and but little affected by 
it. Ifthe natural foundation is loose, porous sand, a layer 
of clay from 4 to 8 inches thick will make a hard and durable 
road. ‘The sand will keep the clay thoroughly drained, and 
the clay, when dry, will form an excellent roadway surface. 
The addition of a small proportion of clean sand will give 
the clay a better consistency in wet weather. Where the 
natural foundation is clay, a layer of sand a few inches 
deep may often be employed with good results. The sand 
will afford protection to the underlying clay, and will form 
a surface which will not become soft and unstable in wet 
weather. 


1694. Forming the Roadway.—The roadway should 
be given a proper crown. Slopes falling outwards each way 
from the center, at the rate of about 1 in 20, with the cen- 
tral ridge rounded off, as shown in Fig. 405, will shed the 

> Vj Yj y Yj water well and make 

OC Pel) 2 2008 form of cross. 

Fic. 405. Section — (formvean a 
roads. The ditches should be made with sides not steeper 
than about 45 degrees, or 1 to 1. Certain special machines, 
commonly called road-machines, are manufactured for 
for the purpose of grading earth roads. The machine con- 
sists essentially of a large steel blade so mounted on wheels 
that it can be adjusted to any desired position with refer- 
ence to the roadway surface. If used intelligently, road- 
machines can be employed to advantage in the construction 
of earth roads and earth foundations of gravel and macadam 


STREETS AND HIGHWAYS. 1037 


roads. The blade of the road-machine makes a clean, uni- 
form cut, giving the surface the proper shape with compara- 
tively little labor. The use of the road-machine should be 
guided by intelligence, however; it can easily be so used as 
to do more harm than good. 

After the roadway is graded, it should be thoroughly 
compacted by rolling with a heavy roller. During the 
process of rolling, all high places should be cut down and 
all hollows filled, so that the finished roadway will have a 
smooth and even, as well as a hard and compact, surface. 
Thorough rolling is very important. If the earth forming 
the roadway be left 1n a ioose condition, to be compacted 
by the wheels of traffic, it will pack unevenly and will be 
more or_less cut up by ruts, which will hold water and cause 
the formation of mud-holes. If, however, the surface is 
thoroughly rolled, it may be made sufficiently firm to sus- 
tain the ordinary traffic, and if kept free from ruts and 
thoroughly compacted, may be capable of resisting the 
penetration of the water, and form a very excellent 
roadway, requiring only occasional repairs. 


MAINTENANCE OF HIGHWAYS. 


1695. Necessity of Constant Attention and 
Prompt Repairs.—In order to maintain a road in good 
condition, it must be given constant care and attention. 
Repairs should be made, not periodically, but whenever 
necessary. The ditches and drains should always be kept 
open and in good working condition, weeds should be cut 
down, and the surface of the roadway should be kept intact. 
This may be done by immediately filling any small breaks 
in the surface, and filling and smoothing over the ruts 
caused by vehicles and the channels washed out during 
storms, then ‘¢horoughly compacting by rolling. Such re- 
pairs should be made promptly and before the damage has 
become serious. This will not only prevent the road from 
getting in very bad condition, but will also make the cost 
of repairs a minimum. 


1038 STREETS AND HIGHWAYS. 


1696. Repairs for Earth Roads.—A road should 
-not merely be put in good condition occasionally, but it 
should be eft in good condition at all times. After long- 
continued rains or the melting of winter snows in the spring, 
the surfaces of earth roads will necessarily become somewhat 
softened and will be more or less cut up by the wheels of 
vehicles. If the roads are in proper condition. at the begin- 
ning of such wet periods, however, and the drains are kept 
well open during its continuance, the injury to the roads 
and the duration of their bad condition will be a minimum. 

As soon as possible after an extended wet period, the 
roads should be put in proper form and thoroughly com- 
pacted by rolling. This should be done while the ground is 
still somewhat moist and yielding, as it can then be worked 
more easily and compacted more closely by rolling than 
after it becomes thoroughly dry and hard. In making re- 
pairs to an earth or gravel roadway, the road machine may 
often be used to good advantage, as it affords a ready means 
of smoothing up the surface. When ruts begin to form 
in a clay road, it is sometimes advantageous to run a 
light smoothing harrow over the roadway and then roll 
thoroughly. 


1697. Repairs for Broken Stone Roads.—Broken 
stone roads will not require repairing as often as earth and 
gravel roads, but they should, nevertheless, have constant 
attention. They should be frequently cleaned of all mud 
and dust. When repairs to the road surface become neces- 
sary, the best method of doing it will depend somewhat 
upon the character of the surface material and the weight 
of the traffic passing overit.. If the surtacesis oieaecere 
material, wearing easily, it should be repaired promptly 
whenever a rut or depression appears. Material of this 
kind binds readily with new material, and repairs may be 
made without difficulty. The new material for repairs 
should be the same as that of the road surface; it may be 
placed upon the roadway in small amounts and compacted 
by the traffic. 


STREETS AND HIGHWAYS. 1039 


Where the surface material is hard and durable, it will 
wear quite evenly and require very little in the way of small 
repairs. But it will not unite readily with a thin coating of 
new material, and when repairs become necessary, it will 
usually be more satisfactory to make more extensive repairs, 
putting on sufficient new material to form an additional 
layer. If only a thin layer of new material is added, it will 
often be.necessary to first break the bond of the old material 
by picking or otherwise loosening it at the surface, so that 
it will firmly unite with the new material. 


1698. Size of Wheels; Wide Tires.—Closely as- 
sociated with the subject of road maintenance is that of the 
size and shape of the wheels on the vehicles that pass over 
the roads. Small wheels and narrow tires have a much 
more injurious effect upon the roadway than do large 
wheels and broad tires. It should also be noticed that 
vehicles with springs have a less injurious effect upon the 
roadway than those having no springs. ‘The exact relation 
between diameter of wheel and resistance of rolling friction 
is not well defined; but the general fact is known that the 
greater the diameter of the wheel, the less will be the resist- 
ance. On this account, and because, also, wheels of large 
diameter have greater bearing surface upon the roadway 
than those of small diameter, the larger wheels have the less 
injurious effect upon the roadway. In this country, how- 
ever, wheels of small diameter are very little used on vehicles 
employed for carrying heavy loads, especially in rural 
districts. 

Wide tires also have a much less injurious effect upon the 
roadway than narrow tires. The wide tires distribute the 
weight over a greater bearing surface, and, the weight being 
the same, the pressure per square inch upon the surface of 
the roadway will be less than in the case of the narrow tires. 
The wide tires do not cut into the roadway and form ruts, 
as do the narrow tires, but, acting as rollers, tend to com- 
pact the roadway. Wide tires would probably not have 
been practicable for the early roads of this country, which 


1040 STREETS AND HIGHWAYS. 


were necessarily very rough, but as the roads become im- 
proved, the use of wide tires on all heavily loaded vehicles 
becomes practicable and very desirable. As is to be expected, 
there is some difference of opinion with regard to how wide 
the wagon tires should be. The best width of tire will de- 
pend upon the weight of the load and the character and con- 
dition of the roadway surface; as these vary greatly, no 
general rule can be stated for the width of tire that will be 
entirely satisfactory. Perhaps as near an approach to a 
satisfactory general rule for the width of tire would: be as 
follows: 


Rule.—7he tires of all freight wagons should have a 
wrath of not less than one inch for each 1,200 pounds of total 
load upon four wheels, or 300 pounds upon each wheel, with a 
minimum width of 24 inches. 


Thus, for a four-wheeled wagon carrying a load of 3 net 
tons, or 6,000 pounds, the width of tire should not be less 


0 
than ae 


= § inches. 
1,200 5 inches 


CITY STREETS AND AVENUES. 


LOCATION AND ARRANGEMENT. 


1699. General Statement of Conditions.—The 
principles of location, construction, and maintenance, as 
relating to ordinary country roads, have been studied in 
the preceding pages. Such applications of the principles 
involved are quite simple. In cities, however, the condi- 
tions are more complex, and, on account of the closer 
limitations and the different interests involved, the problem 
becomes more complicated. Better roadways are required, 
because the traffic is of a heavier character and much more 
dense; and a better class of work is possible, because of the 
more ample means provided. Consequently, the principles 
of good construction must be more rigidly adhered to, 
while, at the same time, their application is generally more 
difficult. The principles which have been studied in their 


STREETS AND HIGHWAYS., 1041 


application to country roads will now be studied in their 
application to city streets. 


1700. Of What the Location of City Streets Con- 
sists.—City streets are not located in the same manner as 
country roads, although the principles governing the loca- 
tion of country roads should also be considered and, so far 
as practicable, complied with in determining the positions 
of city streets. Certain conditions, however, which do not 
affect the location of country roads exert a great influence 
in the location of city streets. In locating a road through 
the country, considerable freedom of choice can usually be 
exercised; the property interests involved will not generally 
be such as to prevent the road from being located in nearly, 
if not quite, the most favorable position with reference to 
construction and maintenance. 

In cities, however, it is quite otherwise. Property is very 
valuable, and, in order to utilize the entire tract to the best 
advantage and make it to the greatest possible extent 
available for business and residence purposes, it is necessary 
that the streets be laid out according to some definite plan 
or system that will give easy communication between all 
parts of the city. Consequently, the position of each street 
must be considered with reference to the positions of other 
streets. To do this is virtually to plan the town site. 
Some of the important matters to be considered in laying 
out town sites will now be noticed. The subject of town 
sites is also treated in the section on Land Surveying, 
which the student should reread carefully before proceeding. 


1701. Purpose and Best Arrangement of 
Streets.—The streets of a city are for the purpose of 
affording direct and easy communication between its dif- 
ferent parts, and giving convenient access to all places of 
business and residence. ‘This, being the purpose for which 
streets are built, is the most important condition to be con- 
sidered, and should be kept well in view in laying out the 
streets of a city. The system of streets should be so 
planned as to give the most direct and easy communication 


1042 STREETS AND HIGHWAYS. 


between all parts of the city, and, at the same time, give 
the greatest amount of frontage available and desirable for 
business and residence purposes. This can generally be 
accomplished by the rectangular system of blocks described 
in the section on Land Surveying. The natural features of 
many localities, however, will require more or less deviation 
from any regular system. The conditions will sometimes 
be such as to require the introduction of diagonal and 
curved streets in a more or less irregular manner. 


BLOCKS AND LOTS. 

1702. Form of Blocks.—The rectangular form of 
blocks can be the most advantageously subdivided into 
building lots, and the streets so formed are convenient for 
communication, if occasional diagonal avenues are provided 
along the lines of most frequent travel extending in such 
directions. The rectangular form of blocks also permits 
such a systematic arrangement of names and numbers that, 
to any one familiar with the system, the locality of a place 
will be evident from its address. 

The form of the blocks will necessarily depend largely 
upon the arrangement of the streets. The introduction of 
diagonal avenues and curved streets into a rectangular 
system will give a more or less irregular form to the blocks 
adjacent to such streets and avenues. Blocks adjoining a 
river or other body of water, or adjoining a railroad that is 
not parallel with the streets, will necessarily be more or less 
irregular also. The form of such irregular blocks will be 
governed wholly by the arrangement of the streets and 
such other matters as must necessarily be considered in 
connection therewith. Where there are no curved or 
diagonal streets or other features requiring blocks of 
irregular form, the blocks should be laid out rectangular 
in form and uniform in size. 


1703. Most Advantageous Form of Blocks.— 
Though the blocks should preferably be rectangular, they 
should not be square. The form of block that is generally 
most advantageous is rather more than twice as long as it 


STREETS AND HIGHWAYS. 1043 


is wide. The distance between streets in one direction 
should only be what is necessary for the proper depths of 
the lots facing upon the two streets, while in the other 
direction the streets need only be close enough together to 
conveniently accommodate the traffic. 

A quite satisfactory form may be obtained for the blocks 
by first laying them out in large squares having the length 
of each side equal to four times the depth of a lot plus the 
width of one street. An intermediate street can then be 
laid out in either direction through the middle of each 
square, thus dividing it into two blocks of a desirable form, 
as shown in Fig. 406. This arrangement is also convenient 
for laying out the diagonal avenues, as, when desirable, the 
intermediate street may be omitted in those squares through 
which the diagonal avenues extend. 












































Fic. 406. Fic. 407. 


The intermediate streets may be laid out in different 
directions through the different squares, when so desired, 
but it is generally much better to have them all extend in 
the same direction, so as to be continuous. 

In order to afford convenient access to the rear of the lots 
for the delivery of merchandise, etc., an alley may extend 
lengthwise through the middle of each block, as shown in 
Fig. 407. Such an alley will be found a great convenience 
in residence blocks, and scarcely less than a necessity in 
business blocks. In any case, the value of the alley as a 
matter of convenience to the occupant of each lot will be 
much greater than would be the value of one-half the width 
of the alley added to the depth of the lot. Comparatively 


1044 STREETS: AND HIGHWAY=s: 


little advantage is to be derived, however, from alleys 
extending across the block. 


1704. Size of Blocks.—The size, as well asthe form, 
of blocks will necessarily depend, to some extent, upon the 
arrangement of the streets. This will be especially the case 
with such irregular blocks as are formed by the introduction 
of diagonal and curved streets. The sizes of such blocks 
will be governed almost wholly by whatever conditions 
require them to be of irregular form, and little else can be 
said with reference to their sizes, except that they should, 
so far as possible, be given such dimensions as can be advan- 
tageously divided into desirable lots. In subdividing them 
into lots, each block should be divided in such manner as 
may be most advantageous for that particular block, but 
with some regard also to the manner in which the other 
blocks are divided. 

Where the blocks are rectangular, their sizes will depend 
somewhat upon the size of the tract that is being laid out, 
for it will evidently be necessary for the sizes of the blocks 
to be such as to advantageously divide up the entire tract. 
If the tract to be laid out is an addition to a city, the sizes 
of the blocks should be governed chiefly by the sizes of the 
blocks and the positions of the streets in the adjoining por- 
tion of the city. When not affected by these conditions, 
the blocks should be uniformly of such size as can be divided 
into lots of the-desired ‘size,. By reference to Fig? 406-it 
will be seen that where there are no alleys through the 
blocks, the width of each block is equal to twice the depth 
of the lots. Where an alley extends lengthwise through 
each block, as in Fig. 407, the width of the block will be 
equal to twice the depth of the lots plus the width of the 
alley. The length of a block may be approximately equal 
to, or somewhat greater than, twice its width, as indicated 
in the preceding article. The length of a block, however, 
must be so adjusted as to be divided into lots of the desired 
width, and must often be modified to accommodate other 
conditions. 


STREETS AND HIGHWAYS. 1045 


1705. Size of Lots.—The sizes of lots vary greatly in 
different cities and often in the different additions of the 
same city. The lots are seldom less than 90 or more than 
160 feet in depth, however, or less than 25 or more than 75 
feet in width. | 

As arule, the lots are larger in small towns and villages 
than in large and densely populated cities. In towns 
situated in agricultural districts, a customary size is 66 feet 
in width by 132 feet in depth (1. e., 4 by 8 rods). On the 
mercantile streets of such towns, there are usually three 
‘¢doors ” or business places to each lot, making the width of 


; 66 Si 
each business place equal to - = gaitect. «In cities. of. can- 


siderable size, 40 feet in width by 150 feet in depth is a 
common size. In large cities, sizes of 25 by 100 feet are 
common. 


STREETS AND AVENUES. 


1706. System of Streets and Avenues.—lIf the 
streets extending in one direction are about twice as far 
apart as those extending in the other direction, i. e., at right 
angles, and the total volume of travel is approximately the 
same in both directions, it is evident that the streets that 
are the further apart should be about twice as wide as 
those that are nearer together, in order to equally accom- 
modate the travel that will come upon them. For each 
one of the streets that are farther apart must accommodate 
about twice as much travel as each one of those that are 
nearer together. Accordingly, these thoroughfares which 
extend in one direction and are at a considerable distance 
apart are made much wider than those which extend in the 
other direction and are nearer together. In such cases, the 
broader thoroughfares extending in one direction are called 
avenues, and the narrower ones extending in the other 
direction are called streets. 

Such a system of streets and avenues is shown in Fig. 408. 
The streets extend in one direction and the avenues in the 
other, with an avenue extending diagonally through the 


1046 STREETS AND HIGHWAYS: 


system. The primary system of square blocks is shown by 
full lines, and the intermediate streets laid out through 
these blocks are shown by dotted lines. Second street is 
shown as continuous through all blocks, but Fourth and 
Sixth streets are not shown continuous through those blocks 
through which the diagonal avenue passes. For the con- 
ditions common to most locations, this is probably the best 
general system that can be devised for laying out streets 


and avenues. In order to suit the conditions of each special 
Avenue D. 









3rd Street. 
6th Street. 
%th Street. 
9th Street. 


5th Street. 


Ist Street. 


_2nd Street. 


eS 
Z] 
Avenue A. 
Fic. 408. 


case, the system should, of course, be more or less modified 
when necessary. 


1707. Complete and Systematic Arrangement 
of Streets; Growth of Cities.—The arrangement of 
the streets should, in all cases, be systematic, both with 
reference to the complete plan and to possible future exten- 
sions ; it should be such as to provide the most direct com- 
munication possible between different parts of the city. In 
order to most conveniently accommodate the travel, each 
street should, if possible, be continuous throughout the 
extent of the city. By causing the travel between different 
parts of the city to take indirect and devious routes, much 
needless inconvenience and waste of time may result from 
an unsystematic and non-continuous arrangement of the 
streets. | 


STREETS AND HIGHWAYS. 1047 


If a city could be laid out complete in the beginning, and 
the requirements of the travel between different portions 
could be foreseen, there would be no difficulty in so planning 
the system of streets as to best accommodate the travel. 
But this is never the case. The growth of cities is often very 
irregular, and it is difficult to foretell either its magnitude or 
its rate. 


ADDITIONS. 

1708. Anticipated and Actual Growth; Addi- 
tions.—In some cases, where large areas have been laid out 
in the anticipation of founding large cities, the expectations 
have not been realized, and only villages or small towns have 
grown up. In such cases, whatever development occurs will 
generally consist in the occupation and building up of a 
portion of the area originally laid out, and will usually 
conform to the original system. 

The more common case, however, is of just the opposite 
nature. in many places, large cities have grown up where 
only small town sites were originally laid out. In suchcases, 
as the growth of the city demands it, additional areas, called 
additions, subdivisions, or extensions, are laid out 
adjacent to the outer limits of the original plot, and, as these 
additions become occupied and built up, the city is still 
further extended by laying out other additions adjacent to 
the outer limits of the older additions. The area of the 
city, as thus developed, will consist of a quite irregular 
patchwork formed by the original plot and the various 
- additions. 


1709. Common Method of Laying Out Addi- 
tions.—Each tract of land laid out as an addition to a city 
will generally represent an individual interest. That is, the 
tract of land, when laid out as an addition, will be owned by 
an individual or by an association of individuals, called a 
syndicate. The owner of the tract, becoming convinced 
that it can be disposed of at a good profit if divided into 
city lots, will proceed to lay it out asanaddition. The chief 
aim of the owner will be so to divide up the tract as to obtain 


1048 STREETS AND HIGHWAYS. 


the greatest possible number of salable lots, regardless of 
all other considerations. 

Unless the matter of laying out new additions to a city is 
regulated by municipal legislation, the streets will seldom 
be continuous and uniform through the different additions, 
but many streets will have jogs or offsets, others will extend 
only through one addition, while others will have different 
widths in the different additions through which they pass. 
The engineer employed to lay out an addition will often be 
required to make his work conform to whatever ideas the 
owner may have formed concerning it, but he should 
endeavor, so far as possible, to make the system of streets 
harmonize with the streets of the adjoining additions. Such 
matters should properly be regulated by municipal legisla- 
tion, but they. seldom are so regulated. The owner of the 
tract generally lays out the addition to suit his own interest 
or convenience, and dedicates the streets to the city; the 
legislative body of the city then usually goes through the 
formality of accepting the addition, without much regard to 
whether it harmonizes with the adjoining additions. 


1710. Example of Liberal Plans; City of Wash- 
ington.—An excellent example of the liberal and system- 
atic arrangement of the streets in laying out the original 
plan of acity, and also of the irregular and unsystematic 
extension of the suburbs is given by the city of Washington. 
The plan of the city was originated by Major L’Enfant, a 
young officer of the engineer corps of the French army that 
aided in this country in the Revolutionary struggle; the 
plan was approved by President Washington, and the city 
was laid out in accordance therewith by Andrew Ellicott, 
about the year 1791. 

The rectangular form of blocks was adopted, and the 
streets were laid out on a very liberal and systematic basis. 
The streets extend north and south, and east and west, 
crossing each other at right angles. From the capital as a 
center, the streets extending east and west are named A, B, 
C streets, etc., in order north and south; while those ex- 


~ 


STREETS AND HIGHWAYS. 1049 


tending north and south are named First, Second, Third 
streets, etc., in order east and west. There is also an 
elaborate system of diagonal avenues, named after the dif- 
ferent States, several of which radiate from the Capitol. 
The generous and extended system of streets and avenues 
indicates that the city was laid out, either with a view to its 
becoming a vast metropolis, or with a very accurate con- 
ception of its future importance and requirements as the 


UY HS | ET | RO / Sw oe DEP Gas | 


eee 


ICME SOO 

_ EDT aSS22 

at) ( JSNOWOOLIUGUU0 ALY ALI oS 1 

SENG SRR Ae Oo 
SCAMS DOAN 
RD Ac ID ooo 


OOS S200 bar 
NO a alls bau Rte 


AJA CULL” 
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ay 














Fic. 409. 


Capital City of the country. At all events, the original plan 
of the city proved adequate for its development during the 
greater part of a century. 

In Fig. 409 is shown a portion of the city of Washington, 
including a part of the original plan, with the adjacent 
suburban additions, Of the area here shown, the portion 
that was laid out in the original plan is easily recognized. It 
consists of a rectangular system of blocks with a quite 


T. IV.—I6 


1050 STREETS AND HIGHWAYS. 


elaborate system of diagonal avenues, generally having open 
squares or circles at their intersections. The streets and 
avenues of this portion are planned according to a quite 
complete and regular system. 

On the other hand, the streets of the suburban additions 
here shown are laid out in a very irregular manner, and are 
wholly without system or harmony. Many of the streets 
are short and inconvenient of access, where they could just 
as well have been continuous and convenient. In some 
cases, the streets of adjoining additions do not connect with 
each other. Asa result of this poor arrangement, property 
in this vicinity must certainly have less value than if the 
streets were laid out according to a regular and _ har- 
monious system. 

All street extensions within the District of Columbia are 
now, however, required by law to conform to the general 
plan of the city of Washington; the effect of this is that 
the regular street lines of the city are gradually being 
extended into the suburbs, and the suburban additions are 
gradually being made to harmonize with the systematic plan 
of ‘the city.. The expense of doing ithis» however mis ai 
doubtedly great; it could easily have been avoided had the 
proper legislation been enacted in time. But the legislative 
bodies did not as clearly foresee the future requirements of 
the city as did the able engineer who laid out the original 
plan. 

GENERAL MATTERS. 

1711. Consideration of Topographical Features. 
—While the arrangement of the streets of a city should be 
such as to give direct and easy communication between, and 
convenient access to, all places of business and residence, 
the arrangement that will best accomplish these ends will 
always depend more or less upon the natural topographical 
features of the locality. The matter of grades must be 
carefully considered—much more carefully even for city 
streets than for country roads. The more important the 
thoroughfare, and the greater the volume and heavier 
the character of the traffic, the more important. becomes the 


STREETS AND HIGHWAYS. 1051 


matter of grades. Steep grades should be avoided wherever 
possible; the grades onimportant thoroughfares, especially, 
should never be steep, if it is possible to obtain easy grades. 
It is much better for an important thoroughfare to be 
located around a hill than over it. If steep grades are un- 
avoidable on some streets, the grades should, if possible, be 
so arranged that the steep grades will occur on comparatively 
unimportant streets. 

In hilly localities, therefore, the consideration of easy 
grades may often require material deviation from the rect- 
angular system of blocks, although, in some cases, it may 
be possible to retain the main features of the rectangular 
system, and so lay out the system of diagonal avenues as to 
allow the main volume of travel to pass around the hills on 
easy grades. 


1712. Curved Streets.—In order to obtain easy or 
even tolerable grades, it will sometimes be necessary to in- 
troduce curved or crooked streets in a more or less irregular 
manner. Curves may often be advantageously employed on 
residence streets to effect a reduction of grades or saving of 
earthwork. In some cases, the esthetic effect may aiso be 
much enhanced by the use of curved lines for the streets. 
The direction of the street should never be changed by an 
abrupt bend, except at the intersection of another street. 
Where curves and other irregularities in the arrangement 
of the streets occur, great care should be exercised to avoid 
the introduction of short streets in an irregular manner. 
In all cases, the streets should be, so far as possible, con- 
tinuous, and the arrangement should adhere as closely as 
possible to some well-defined system. The straight and 
curved streets should be arranged harmoniously. 


1713. Parks.—The fact that growing vegetation is an 
important factor in purifying the air makes it desirable that 
parks be laid out at frequent intervals throughout the 
densely populated portions of a city. It is not necessary 
for these parks to be large and elaborately laid out, but they 
should be numerous, to serve as fresh-air spaces in the 


1052 STREETS AND HIGHWAYS. 


crowded portions of a city. The smail triangular pieces 
cut off by the intersection of diagonal streets, or other 
irregularly shaped pieces not suitable for buildings, can 
very advantageously be laid out as small parks. Such 
parks, though they consist only of grass lawns containing a 
few trees, will serve to ornament the city and considerably 
raise the value of adjacent property, and, at thé same 
time, will tend to keep the air in the vicinity purer than it 
otherwise would be. 

At suitable localities throughout the city, entire blocks, 
and even much larger tracts, should be laid out as parks. 
Blocks of irregular shape, such as those formed by curved 
and diagonal streets, should generally be selected. Such 
blocks will not only be less advantageous for building upon, 
but will also generally present a better appearance when 
laid out as parks than will the blocks of rectangular form. 
Tracts of ground that are too rough and precipitous to be 
conveniently built upon are quite suitable for parks, and can 
generally be devoted to such purposes with excellent results. 


MATTERS RELATING TO PRACTICAL FORM | 
AND DETAILS. 


WIDTH OF STREETS. 

1714. Importance of Great Widths.—The width 
of ‘city streets 1s a’ subject that does not receive the.con- 
sideration it properly deserves. The subject is very im- 
portant, not only as relating to the convenience of travel, 
but also as affecting the health and comfort of those whose 
residences or places of business occupy the streets. For, in 
closely built-up districts, the width of the streets will 
practically determine the amount of light and air that 
can penetrate into the buildings. The width of street 
here referred to is, of course, the total width between 
property lines. It is often the case that convenience to 
travel is the only condition considered in laying outa street, 
and this is but imperfectly considered; if the street is wide 
enough to accommodate the travel that is likely to come 


STREETS AND HIGHWAYS. 1053 


upon it, then it is thought to be wide enough forall possible 
purposes, and no other condition is thought to be of suffi- 
cient importance to be considered. This, however, is a 
great mistake, for all conditions affecting the health and 
comfort of the residents are of great importance and should 
be carefully considered. 


1715. The Usual Widths.—In the different cities of 
this country, the streets and avenues are laid out in various 
widths, but generally between the minimum and maximum 
limits of 50: and 200 feet. Widths of 60, 66, 75, 80, and 
90 feet are commonly used for streets, and the widths of 
avenues are commonly 100, 120, 125, 150, and 160 feet. 


1716. Streets Are Commonly Too Narrow.—In 
nearly all the large cities, the streets, as laid out, are too 
narrow. They are generally quite overcrowded by the 
travel. In closely built up districts, they are also usually 
quite dingy; the adjoining buildings have meager hght and 
insufficient ventilation, and are often more or less damp. 
Such conditions are evidently quite unsanitary. They prevail, 
to a great extent, on streets of large cities that are closely 
built up with tall buildings. Property adjoining such 
streets certainly can not be as valuable as though the streets 
were wide enough to permit air and light to penetrate freely 
into the buildings. 

The reason that the streets of large cities are so com- 
monly narrower than they should be is chiefly because the 
future of a city can not be foreseen when the streets are laid 
out. In many cases, what had been laid out for an ordinary 
town has developed into a great city, requiring many new 
additions and extensions to be laid out. Each new addition 
is commonly laid out merely as a residence suburb, and if, 
as is usually the case, there is no law regulating suburban 
extensions, the owners of the property, interested only in 
getting as many salable lots out of it as possible, will gen- 
erally make the streets as narrow as possible without injur- 
ing the sale of the lots. As long as the tract so laid out re- 
mains an uncrowded residence suburb, with residences set 


1054 STREETS AND HIGHWAY: 


well back from the street and having spacious lawns, the 
narrow streets will be reasonably satisfactory. During the 
growth of the city, however, the nature of many localities 
will become materially changed. Districts devoted to trade 
will be occupied by manufacturing plants, the mercantile 
interests will encroach upon the inner residence districts, 
and the sparsely settled suburbs will become closely built up 
residence districts. The width of street sufficient for the 
uncrowded suburbs with residences set well back from the 
street will be quite unsatisfactory for the closely built up 
district with houses set out to the property line. It would 
be still less satisfactory if the streets were built up solidly 
with very tall buildings. 


1717. Widthsin the City of Washington.—-In the 
city of Washington, the streets are generally 70, 80, 90, 100, 
and 110 feetin width, though one important street is 160 feet 
wide, and one short, unimportant street is only 40 feet wide. 
Almost all the avenues are 160 wide, though a few have 
widths of 130, 120, and 85 feet. The law now requires that, in 
laying out new streets and avenues, the width shall not be 
less than 90 feet for streets or 120 feet for avenues, interes 
mediate streets, called places, may be laid out within blocks 
with a width of 60 feet, but the distance between full width 
streets must not be more than 600 feet. This city probably 
has the best and most liberal system of streets of any Ameri- 
cancity. The beneficial results of its liberal policy with re- 
gard to streets are evident in itslarge growth and popularity 
as a residence city, and the corresponding property values, 
as well as in the greater comfort of its inhabitants. 


1718. Suitable Widths for Streets.—In cities of 
large size, where the houses are built closely together and 
extend out to the property line, the residence streets should, 
if possible, have widths of not less than from 80 to 100 feet, 
in order to present a good appearance and afford plenty of 
light and air. For outlying suburbs with ijarge lawns, a 
width of 60 feet may be satisfactory for the streets, thougha 
greater width is to be preferred. In large cities, however, 


STREETS AND HIGHWAYS. 1055 


such suburbs are always liable to become densely built up 
districts, and for such cities a greater width is very much to 
be preferred. Moreover, a lot 120 feet deep upon a street 80 
feet wide will generally be more valuable than a lot 130 feet 
deep upon a street 60 feet wide. 

As a rule, important commercial thoroughfares should 
never be less than 100 feet in width, and, if lable to be 
occupied by street-railway tracks or bordered by very tall 
buildings, they should be much wider. In many towns, a 
width of 4 rods, or 66 feet, is adopted for all but the more 
important streets, and this is a reasonably satisfactory width 
for streets that are never liable to become thoroughfares of 
commerce. ‘That is, it isa fairly good width for the resi- 
dence streets of towns that are so situated as not to be likely 
to ever become important commercial centers. For really 
satisfactory and desirable streets, however, greater width is 
necessary. 


THE ROADWAY. 


WIDTH AND CROSS-SECTION. 
1719. Width of Roadway.—What is said above 
relates to the total width of streets between property lines. 
This width will not necessarily be wholly occupied by the 
pavements. Indeed, except in important business thorough- 
fares, it is seldom that the entire width of a street is occu- 
pied by the roadway and sidewalks. As the width of these 
can be easily changed whenever the pavement is renewed, 
they should always correspond with the immediate require- 
ments of the traffic passing over them. ‘The width should, 
of course, always be sufficient to easily accommodate the 

traffic, but widths materially greater are disadvantageous. 
The width of the roadway should be such that it will a// 
be used. The width necessary to accommodate the traffic 
will, of course, depend upon the volume and character of the 
latter. A width of 80 feet will usually be sufficient for the 
roadway of a crowded commercial thoroughfare in a large 
city, while a width of 60 feet will accommodate the traffic of 


1056 STREETS (AND HIGHW ferme. 


a very important business street. For many -business streets, 
a width of 50 feet will be ample for the roadway, while 
for others, a widthof 40 feet will be sufficient. For residence 
streets, the width of roadway should generally be from 24 to 
36 feet, according to the importance of the street and its 
position with reference to the routes of greatest travel. The 
widths of the roadways on important residence streets of an 
American city of about 100,000 inhabitants are being re- 
duced, as the streets are paved, from 34 to 30 feet; the for- 
mer width having been found to be greater than is required, 
considerable saving in the cost of paving and maintenance 
is effected by reducing the width. When no portion of the 
roadway is occupied by street-railway tracks, a width of 24 
feet will accommodate a very large amount of light driving, 
and will be sufficient for many residence streets not situated 
along the main lines of travel. Even less width will some- 
times be sufficient for roadways in smalltowns and villages. 
On streets of light traffic, the roadway should be narrowed 
to the width really required; this will beadvantageous rather 
than otherwise, as it will often permit the narrow roadway 
to be improved much more than it would be possible to 
improve the wider roadway with the funds available. 


1720. Cross-Section of Roadway.—lIn its relation 
to country roads, this subject was noticed in Art. 1672. 
What is here stated relates more particularly to the cross- 
section of citystreets. Experience has shown that it is 
necessary to provide gutters or side ditches along the outer 
edges of the roadway, in order to carry away the surface- 
water, and that, in order that the water falling upon the 
surface of the roadway may be thrown off into the side gut- 
ters, the center of the roadway must be made higher thanits 
outer edges. The form of cross-section that will best 
accommodate these conditions will depend chiefly upon the 
character of the roadway surface and the nature of the traffic 
sustained upon it. 

Before a roadway is paved, its cross-section will havea 
more or less irregular form and will but roughly approx- 





STREETS AND HIGHWAYS. 1057 


imate any theoretical figure. Unpaved roadways, however, 
are generally so laid out and graded as to more or less closely 
approximate some theoretical form of cross-section. When 
a street is paved, it is givena definite cross-section, the form 
of which will depend upon the kind of pavement, the grade 
of the roadway, the nature of the traffic, and the ideas of 
the engineer in charge of the work. Some kind of gutter is 
always provided along each outer edge of the roadway, and 
the roadway between the gutters is elevated by giving ita 
convex form. The elevation given to a roadway between 
the gutters iscalled the crown, and a roadway so elevated 
is said to be crowned. 





CROWN. 

1721. Amount of Crown.—The highest point in the 
crown of a roadway, that is, the highest point in the surface 
line of its cross-section, will here be called the summit of 
the crown. The height of thesummit of the crown above 
a straight line through the outer edges of a roadway, or 
bottoms of the gutters, will be designated as the amount of 
crown, and also asthe height of crown. The amount of 
crown necessary to efficiently throw off the surface water 
into the side gutters and, at the same time, cause no incon- 
venience to the traffic, will depend chiefly upon the character 
of the roadway surface andits grade. The crown or lateral 
slope of the roadway should never be so great as to cause 
inconvenient tipping of vehicles in driving on the side of the 
roadway, as this would cause the traffic to follow the center of 
the roadway, with the effect of rapidly wearing away that por- 
tion and destroying the crown. The more smooth and per- 
fect the roadway surface, the more easily will the water flow 
off, and, consequently, the less will it need to be crowned. 
Well-paved streets will require much less crown than 
ordinary earth roads. 

For paved roadways, the crown, or lateral slope, should 
be less on steep than on flat or level grades. This will 
make the roadway surface somewhat less slippery and in- 
convenient for travel on steep grades, while there will gen- 
erally be no difficulty about the water reaching the gutters 


1058 STREETS AND HIGHWAYS. 


without damage to the roadway, if it is paved. On the 
other hand, for an earth or gravel roadway that would be 
liable to become damaged by the water following the road- 
way and washing out gulleys and channels in flowing down 
steep inclines, the crown, or lateral slope, of the roadway 
should be zucreased on steep grades, in order to more 
quickly throw off the water into the side gutters and, so far 
as possible, prevent it from flowing down the roadway. In 
spite of such precaution, however, if the roadway is not con- 
stantly kept in good repair, water will flow along in the 
wheel ruts and in the depressions worn by the horses’ feet, 
and do more or less damage on steep inclines. 


1722. Formula for Amount of Crown.—It is im- 
possible to express the above conditions in exact mathemat- 
ical formulas. Hence, no really satisfactory formula for 
the amount of crown can be given. As the amount of 
crown should generally be proportional to the width of road- 
way, however, we may write, for a comparatively level 
grade, the formula 





70g —1 
C= [7 +2" ao , (205.) 


in which ¢c is the amount of crown, or height of the center 
of the roadway above its outer edges; w is the width of the 
roadway; fis the per cent. of grade, or rise per 100 units 
(usually feet) of horizontal length, and gq is a coefficient 
relating to the character and condition of the roadway sur- 
face. No. exact; values-can be voiven fons tom direc 
kinds of roadways, however, it may generally have values 
about as given in the table of Coefficients for Roadway 
Crowns (Tables and Formulas). 


For ‘a level grade, 7 =o. andi yew. 


1723. Exampie.—(a) A common earth roadway 24 feet wide 
has a grade of 5 per cent. How much crown should it have ? 


SOLUTION.—As given in the table referred to in the preceding 
article, the value of g fora common earth roadway is 7. By apply- 


STREETS AND HIGHWAYS. 1059 


ing formula 205, and using this value of g, the required amount of 
crown is found to be 


a4. 24K 5X G—D) _ wor 
att ae BGs ee of afoot. Ans. 


EXAMPLE.—(4) A roadway 48 feet wide, paved with asphalt, has a 
grade of 1.44 per cent. How much crown should it have ? 


SOLUTION.—By applying formula 205, and using the value of gas 
given for asphalt in the table, the required amount of crown is found 


to be 


48 48x 1.44 x (5 —1) __ 
Ties Bae SO La .064 of afoot. Ans. 


EXAMPLES FOR PRACTICE. 
1. A roadway 35 feet wide, paved with wooden block pavement, 


has a grade of 6 per cent. How much crown should it have ? 
Ans. 0.50 ft. 


2. An ordinary gravel roadway 20 feet wide hasa grade of 4 per 
cent. How much crown should it have? Ans. 0.44 ft. 


3. A roadway 60 feet wide, paved with brick, hasa grade of 2 per 
cent. How much crown should it have ? Ans. 0.555 ft. 


4. A common earth roadway 16 feet wide has a grade of 9 per cent. 
How much crown should it have ? Ans. 0.535 ft. 


5. A broken stone roadway 24 feet wide has a grade of 3 per cent. 
How much crown should it have ? Ans. 0.415 ft. 
6. A roadway 36 feet wide is paved with granite block pavement. 

If it has a grade of 4 per cent., how much crown should it have ? 
Ans. 0.36 ft. 


1724. Form of Crown.—With reference to the man- 
ner in which the crown of the roadway is effected, two 
different forms of cross-section are advocated and used. 

In one form, the surface line of the cross-section is the 
arc of acircle or a similarcurve. This form of cross-section 
is shown in Fig. 410; it will here be designated as a curving 
crown. As will be noticed in the figure, a considerable 
portion of the roadway surface adjacent to the center, in 
this form of cross-section, is nearly level, while near the 
outer edges the lateral slope of the roadway is quite steep. 
The tendency of this will be to cause the greater part of the 
traffic to follow the center of the roadway, producing the 
greatest wear upon that portion. 


1060 STREETS AND HIGHWAYS 


In the other form of cross-section, the surface line consists 
of two straight lines having the proper inclination and con- 
nected by a short curve at the center of the roadway, as 


Yili 
NS 


OOM. UY YUYU&mgygyKxs4j;zjyn Y 
VI a 
Fic. 410. 

shown in Fig. 411. The length of the curve at the center 
is generally made about five feet, or a little more than the 
width of anordinary carriage. In this form of cross-section, 
which will be designated as a sloping crown, the lateral 
slope of each side of the roadway extends uniformly to the 
gutter, and the width of the nearly level portion at the 
center is greatly reduced. This obtains a more efficient 
drainage, and, at the same time, permits teams to drive near 





a w. — 
ay tj (SALTED A Wb lsd fli tiys tig sess 22p99- ia 
LZ Mis 
Y/Y Wf Y////7 YH YW . Y/ 
Fic. 411. 


the curbing with nearly as much comfort as upon any other 
portion of the roadway. 


1725. Elevations on Cross-Section.—In laying out 
the cross-section of a roadway, it is necessary to determine 
the elevations of the surface at different points across the 
roadway. In nearly all cases, whether the roadways have 
curving or sloping crowns, the summit of the crown is at the 
center of the roadway, and the slopes of the sides are 
symmetrical with reference to the center... uch a, crows 
will here be called a symmetrical crown. In this and 
the three following articles, symmetrical crowns only are 
considered. 

The grade line of roadway represents the elevation of the 
summit of the crown. Consequently, for any cross-section 
having a symmetrical crown, the elevation of the roadway 
surface at the center is given directly by the grade line, and 
the eievation of any other point in the surface of the cross- 
section must be: referred, tothe cievation, of otade mre 


STREETS AND HIGHWAYS. 1061 


elevation of any point in the surface of the cross-section, 
other than the center or summit, must be determined by its 
distance below the grade line. Thedistance of any point in 
the surface of the cross-section below the grade line, or 
summit of the crown, may be easily determined by means 
of the rectangular coordinates of the point, taking the 
origin of the summit of the crown. (See Arts. 1464 to 
1472.) 


1726. Coordinates to Curving Crown.—For a 
cross-section having a curved surface line, as shown in 
Fig. 410, 2 good form is given by a circular curve. The 








equation of the curve, however, will be more simple for a 
parabolic than for a circular curve, and as, for so flat an arc, 
the two curves will be practically identical, the parabolic 
curve will be used. With this curve, if + and y are, respect- 
ively, the abscissa and ordinate to any point / in the surface 
line of the cross-section, with the origin at the center 0, as 
shown in Fig. 412, the value of y for any corresponding 
value of 1, or, in other words, the distance of the given point 
below a horizontal line tangent to the roadway surface at 
the center, will be given by the formula 


ett x? 


S Deraae rr eae (206.) 





in which ¢ is the amount of crown, and w is the width of 
roadway, both in feet, as shown in Fig. 412. In this 
figure, the amount of crown is, for clearness, somewhat 
exaggerated. 


1727. Coordinates to Sloping Crown.—A cross- 
section having a symmetrical sloping crown is shown in Fig. 
413, the amount of crown being somewhat exaggerated. In 
this figure, as in Fig. 412, cand ware, respectively, the crown 
and width of the roadway, while x and y are the abscissa and 


1062 STREETS AND HIGHWAYS, 


ordinate, respectively, of any point f inthe surface line of 
the cross-section, with reference to an origin at the center 0 
of the roadway. The two sides of the roadway, or portions 
tg and ?@ g' of the surface line of the cross-section, have a 
uniform slope, while the portion ¢ ¢’ or 6 is a short parabolic 


curve which joins the two slope lines and is tangent to them. 


oy 







| ea Rae SES aL oS re te ee ee Le i 
FIG. 413. 


The rate s of lateral slope for these uniformly sloping 
portions of the roadway surface is given approximately by 
the formula 
ee 7 
Oe ah 


(207.) 


The coordinates of any point on the curved portion of 
the cross-section are given by the formula 
eh 


At the tangent point ¢, where the curve portion of the 
surface line joins the straight slope line, the abscissa + will 


b ces ib ae 
have the value —; by substituting this value for x in formula 


6)? 
208, and reducing, the ordinate becomes 


b 
y= —. (209.) 
The coordinates to any point f along the straight slope 
line ag will be given by the formula 


ens (« = ) (210.) 


This formula may, if desired, be used instead of formula 
209; for, at the tangent point 7, the abscissa x will be 
b 
9” 
will reduce it to the form of formula 209, 


equal to —, and this value substituted for + in formula 210 


STREETS AND HIGHWAYS. 1063 


rine EXAMPLE.—(a) If the roadway described in example (a) 
of Art. 1723 be given the amount of crown as there determined, in 
the form of a curving crown, what will be the ordinate to a point 
in the surface line of the cross-section distant 8 feet from the center of 
the roadway ? 


SOLUTION.—The width of the roadway, as given in the example 
referred to, is 24 feet, and the crown is .7125 of a foot; the abscissa +, 
or distance of the given point from the center of the roadway, is 8 feet. 
By formula 206, which applies to curving crowns, the value of the 
4 .'7125 « 8? 

942 


ml = .3167 of a foot, very nearly. 


ordinate y is found to be 
Ans. 


EXxAMPLE.—(é) If the roadway described in example (2) of Art. 1723 
be given the amount of crown there determined, in the form of a slo- 
ping crown, what will be the ordinate to a point in the surface line of 
the cross-section 15 feet from the center of the roadway, assuming the 
length 6 of the central curve to be 5 feet ? 


SOLUTION.— The width of the roadway, as given in the example 
referred to, is 48 feet, and the crown is .364 of a foot; the abscissa +, 
or distance of the given point from the center of the roadway, is 15 feet 
and the length 4 of the central curve is 5 feet. By applying formula 
207, the rate of slope s in the uniformly sloping portion of the cross- 

4X .364 
2x 48 —5 
By applying formula 210, the value of the ordinate to a point in the 
roadway surface 15 feet from the center is found to be 


section is found to be = .016 of a foot per horizontal foot. 


y = .016 (15 — $) = .22 of a foot. Ans. 


EXAMPLES FOR PRACTICE. 

Note.—The following examples relate to those given in Art. 1723. 
In each case, the width of roadway and amount of crown will be taken 
as given in the corresponding example of that article. The results 
will not be carried bevond the fourth decimal place. 

1. If the roadway of Example 1 be given a curving crown, what will 
be the values of the ordinates to the surface line at points in the cross- 
section, distant, respectively, (a) 2.5 feet, (4) 5 feet, (c) 10 feet, (d) 15 
feet, and (¢) 17.5 feet from the center ? (a) .0102 ft. 

| (6) .0408 ft. 

Ans. (c) .1683 ft. 
(d) .3673 ft. 

(2) .5000 ft. 

2. If the roadway of Example 2 be given a sloping crown, with a 
central curve 8 feet in length, what will be the values of the ordinates 
to the surface line of the cross-section at points distant (a) 4 feet, 


1064 STREETS AND HIGHWAYs: 


(4) 8 feet, and (c) 10 feet from the center? (@) What will be the rate s 
of the uniform side slope ? (2) late 
(6) .38 ft. 
(c) .44 ft. 
(2) .055 ft. 


3. If the roadway of Example 3 be given a sloping crown, witha 
central curve 9 feet in length, what will be the ordinates to the surface 
line of the cross-section at points distant (a) 3 feet, (0) 4.5 feet, (c) 10 
feet, (2) 15 feet, (2) 20 feet, and (/) 25 feet from the center? (g) What 
will be the rate s of the uniform side slope ? (az) .020 ft. 

(6) .045 ft. 
(2) Looe 
Ans. 4 (@) .255 ft. 
(e) .355 ft. 
(f) .455 ft. ~ 
(zg) .020 ft. 


4. If the roadway of Example 4 be given a curving crown, what will 
be the ordinates to the surface line of the cross-section at points distant 
(a) 4 feet, and (0) 8 feet from the center ? nes ( (a) .1888 ft. 

( (0) .585 ft. 


5. If the roadway of Example 5 be given a sloping crown, with a 
central curve 8 feet in length, what will be the ordinates to the surface 
line of the cross-section at points distant (a) 4 feet, (4) 6 feet, (c) 8 feet, 
and (@) 10 feet from the center? (é¢) What will be the rate s of the 
uniform side slope? (a) .088 ft. 

(0) .166 ft. 
Ans. { (¢) .249 ft. 

(@) .382 ft. 

(e) .0415 ft. 

6. If the roadway of Example 6 be given a sloping crown, with a 
central curve 8 feet in length, what will be the ordinates to the surface 
line of the cross-section at points distant (a) 4 feet, (4) 8 feet, (c) 12 feet, 
and (@) 16 feet from the center? (¢) What will be the rate s of the 
uniform side slope? (a) .045 ft. 

(6) .135 ft. 
Ans. (c) .225 ft. 

(d) .315 ft. 

(2) .0225 ft. 


Ans. 


GUTTERS AND CURBING. 

1729. Gutters.—As has been previously stated, some 
kind of an open channel must be provided along each side 
of a roadway, to receive the water from the surface of the 
roadway and convey it toa drainage outlet. Side ditches, 


STREETS AND HIGHWAYS. 1065 


such asare shown in Figs. 400, 401, 404, and 405, would be 
unsightly, dangerous, and otherwise impracticable for 
crowded city streets. For the purpose of surface drainage 
in city streets, therefore, those portions of the roadway 
adjacent to each outer edge are given such form as to serve 
as gutters for conveying the water from the surface of the 
roadway. ‘These gutters are made so shallow as to still be, 
to some extent, available for driving purposes when not 
required for drainage purposes. 


1730. Forms of Gutters.—Various forms of gutters 
are used; three different forms are quite common. The 


YY 
—Ao-— 


® 


Lie. 











FIG. 414. 


form shown in Fig. 414 is the simplest and, all things con- 
sidered, is probably the most advantageous for well-paved 
roadways. It is very commonly used with the best pave- 
ments. Inthis form of gutter, the crown of the roadway 
is continued regularly to the curb line, the gutter being 
formed by the angle between the sloping surface of the 
roadway and the vertical side of the curbing. The full 
width of the roadway is thus left available and convenient 
for driving. The form of roadway shown in Fig. 415 is the 
same as that shown in Fig. 414, except that the bottom g 


Mlddlllldddidua 7/7 





Fic. 415. 


of the gutter is made level. Little, if any, advantage is 
gained by this, however, and the form of gutter is not 
generally as good, nor is it nearly as extensively used, as 
the form shown in Fig. 414. Where the gutters are paved 
with cobblestones, the form shown in Fig. 416 is very com- 
monly employed. When a substantial stone curbing is 
used, it is doubtful whether any advantage is gained by 
this form of gutter, while it possesses the disadvantage of 


T. 1V.—17 


L066 STREETS AND HIGHWAYS. 


narrowing the available driveway w’ and also of making it 
inconvenient for carriages to drive close to the curbing. 
For convenience of reference, the forms of gutters shown 


YY), MEH i 
7 Ld 


a ——_— 
Fic. 416. 


in Figs. 414, 415, and 416 will hereafter be designated as 
forms a, 6, and c, respectively, as marked in the figures. 


1731. Width of Gutter and Crown.—lIn Figs. 415 
and 416, zw’ is the width of the crowned portion of the road- 
way, or width between gutters, while g and yg” are the 
widths of the two gutters. The width of gutters is some- 
times made equal to the amount of crown, although they 
are quite commonly made materially wider. It is evident 
that for gutters of forms 6 and c the crowned width of the 
roadway w’ will be equal to the total width of the roadway 
minus the width of the two gutters, or—when the width of 
gutter is made equal to the crown—minus twice the amount 
of crown. 

In applying formula 205 for determining the amount of 
crown in roadways having gutters of forms 6 andc, the full 
width of the roadway between curbing may be substituted 
for w, but in applying formulas 206 or 210 for obtaining 
the ordinate at the gutter, the abscissa + should, of course, 

zw’ 


be taken equal only to one-half the crowed width, or oe 


1732. Height of Curbing.—Flat stones or planks 
are usually set on edge along the borders of the roadway, 
as shown at e, ein Figs. 414, 415, and 416. These are 





Fic. 417. 


called curbs or curbing. In some cases, earth or gravel 
roadways have gutters paved with cobblestone where no 
curbs are set. In such cases, a good substitute for curbing 


STREETS AND HIGHWAYS. 1067 


may be formed by the cobblestone pavement, as shown in 
Fig. 41%. The stones are usually set vertically on edge, 
but are sometimes set somewhat sloping. 

The curbing is generally placed at the same height as 
the center of the street. In other words, the top of the 
curbing is usually set to the grade line adopted for the 
Street. 


FOOTWALKS AND STREET LAWNS. 


1733. Sidewalks arc constructed of different ma- 
terials, such. as gravel, wood, brick, stone, concrete, asphalt, 
etc., and are generally given such widths and placed at such 
heights as will best accommodate the conditions of each 
case. 


1734. Widths and Heights of Sidewalks on 
Business Streets.—On business thoroughfares, the entire 
space between the curbing and the building line is usually 
occupied by the sidewalk, which commonly consists of stone 
or other substantial material. ‘The edge of the sidewalk 
adjacent to the curbing is always placed at the same elevation 
as the curbing, 1. e., at grade, but the edge adjacent to the 
building's is elevated somewhat above this, giving it a slight 
inclination towards the gutter for the purposes of drainage. 


1735. Widths and Heights of Sidewalks on 
Residence Streets.—On residence streets, the construc- 
tion of sidewalks does not follow any rigid rule; they are 
generally given widths of about one-fifth to one-sixth the 
widths of the roadway, or from about 5 to 10 feet. Dif 
ferent materials are used in their construction. Wooden 
sidewalks consist of a wearing surface of planks extending 
crosswise of the walk and spiked to longitudinal stringers. 
These walks are generally made of such widths that the 
planks will cut from the commercial lengths of planks with- 
out waste. Widths of 4 feet 8 inches (which will cut from 
a 14-foot plank), 5 feet 4 inches (which will cut from a 16- 
foot plank), 6 feet, 8 feet, etc., are commonly used for 
plank sidewalks. When these are replaced by walks of a 
more substantial nature, the same widths are often retained. 


1068 STREETS AND HIGHWAYS. 


The outer edges of the sidewalks on residence streets are 
commonly placed about 2 feet from the fence line. 

The sidewalks of residence streets are generally placed at 
grade wherever the natural cross-section of the street is 
sufficiently level for this to be done without inconvenience 
or disadvantage to the adjoining property. It is decidedly 
the best practice to put @// sidewalks either at grade or at a 
certain small fixed distance (3 or 4 inches) above grade; 
this is especially true of the sidewalks of paved streets. In 
many cities, however, the elevations of the sidewalks in 
residence districts are varied materially from the street 
grades wherever such variation will better accommodate 
the adjoining property. This is illustrated in Fig. 418, in 


FR oy 


DID 
ph Ages 
ms 
“BS ge 


Vie, 
2 


egy pe 
ws 


é€ 


y 











t 
i] 
13 
iy ELORFRL SSS v7 
FET 7s 
g| tll CE FIR Le 
*~ vs) See 1 eee 1 
>| 
i. 
! 
Qi 
S 
ie 
Ay 
Fic. 418. 


which, in order to accommodate the elevated position of 
the adjacent property, the sidewalk on one side of the street 
is elevated considerably above the surface of the roadway. 
This practice should be avoided whenever possible, as the 
resulting appearance of the street is not nearly as good as 
when both sidewalks are placed at grade. This is a matter 
that is not usuaily left wholly to the discretion of the munic- 
ipal engineer, however, but is often regulated by city 
ordinance, or, possibly, by some provision of the city charter. 


In such cases, the engineer must be governed by such regu- 
lations as may exist. 


1736. Lateral Slopes of Sidewalks.—For the pur- 
pose of drainage, sidewalks should have a slight lateral slope 


STREETS AND HIGHWAYS. 1069 


towards the curb. On closely built up business streets, in 
which the entire width between the curb and the building 
line is occupied by the sidewalk, this lateral slope of the 
sidewalk will fix the elevations on the building line. The 
edge of the sidewalk adjacent to the curb will be placed at 
the elevation’ of the curb, that is, at the street grade, and 
the edge of the sidewalk adjacent to the building line willbe 
higher or above grade an amount equal to the width of the 
sidewalk in feet multiplied by the lateral slope per 
foot. In some cities, a lateral slope of .24 per cent., or 
1 in 40, is given to the sidewalks; a slope of 2 per cent., 
or 1 in 50, however, is generally very satisfactory for this 
purpose and will here be adopted for all problems. All that 
portion of the street between the curb and the property line* 
should be given this uniform lateral slope, whether wholly 
occupied by the sidewalk or not. 


1737. Street Lawns.—Those portions of a residence 
street not occupied by the roadway and sidewalks should be 


GM ad 


1h 4 iii 












© 
x 

S YY Q 
ter ; 
I & 

$ 80° $ 
3 > 
= 

£ 


FIG. 419. 


laid out as lawns, with at least one row of trees on each side 
of the roadway. In Fig. 419 is shown the cross-section of a 
residence street 80 feet wide, having a roadway 40 feet in 
width, and two sidewalks each 8 feet inwidth. A single row 


* The boundary line of a street, or dividing line between the street 
and the adjoining property, is known variously as the property 
line, building line, block line, fence Line, and, some- 
times, street line, though the latter term is more commonly ap- 
plied to the center line of the street. 


‘Top “Old 


1 
\ 





pac a PrN 





“4 
SS 


STREETS AND HIGHWAYS. 


0 


qadong 


wz 


euyyT 





‘Och “VIA 





ae 











Dace eee se re . 
ep r 766 102 ! G6 


YY : Yi) 
4, J HE, > 
Yj ED. LES Vj, Yj COG Ye ‘ig YY, UY 
MELEE SM OWAAY 4 EES j COO $ 
LESSEE LLESOMEZ, VL PY //Lis Pra ai Yl 
\) 














aurqy fizsadodd 


Z 

Ce CNW, yar ~~ 

re we oe vo 
‘ede, , 


“iy ny 
Ba sd 






aurT fhysadordss 


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yi a d 
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Bh 1S & 5,25 
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AF 5 
Win “yd 
Deen S 
- 





| 


eurvT fipvadold 


STREETS*AND- HIGiWAYS, 1071 


of trees is shown on each side of the roadway, between the 
sidewalk and the curbing. With these widths, however, if 
the residences are set well back from the property line, 
another row of trees could be advantageously introduced 
between the sidewalk and the property line. 

In cases where the lawns are of large widths, two rows of 
trees are sometimes set along each side of the roadway be- 
tween the sidewalk and the curbing, as shown in Fig. 420, 
which represents the cross-section of an avenue 120 feet 
wide, having a roadway 50 feet wide and two sidewalks 
10 feet wide each. The arrangement there shown is gener- 
ally well adapted to avenues of this width. Other arrange- 
ments are, of course, employed. In some cases, the sidewalk 
is placed nearer the curbing, leaving most of the lawn space 
between the sidewalk and the property line. This is not as 
good an arrangement as that shown in Fig. 420, however, 
because the position of the sidewalk is neither as pleasant 
for pedestrians nor as conveniently accessible to the resi- 
dences. Very broad avenues sometimes have two roadways, 
which are separated bya lawn extending along the center of 
the avenue and containing one or two rows of trees. Such 
very broad avenues are called boulewards. The cross- 
section shown in Fig. 421 is somewhat similar to that of the 
Western Boulevard, New York City. 

The importance to a city of clean and well-kept lawns can 
scarcely be overestimated. They serve not only as a means 
of ornamentation, but also as a means of purifying the air, 
and thus have a beneficial effect upon the health of the 
inhabitants. 


STREET INTERSECTIONS. 


DIFFICULTIES ENCOUNTERED. 


1738. Different Elevations of Curb Angles.—The 
proper arrangement of the grades at street intersections is 
often a quite troublesome matter. Where two streets in- 
tersect, it is quite desirable that the crown of each street 
should be continuous to the center of intersection. It would 


1072 STREETS AND HIGHWAYS. 


also appear desirable for the grade of each street to continue 
uniform to the center of intersection, but this is a matter 
often involving considerable difficulty. In Fig. 422, 4 Band 
C Dare the “center lines*of two-streetsuntersectinoweaca 
other at right’ angles: “Che: points aye.e,-andeerarestne 
angles of the curbing, and are called curb angles, or curb 
corners. Instead of being really angles, however, as 
shown in the figure, they are often the quadrants of small 
circles. ‘Let it be assumed* that’ the total widths oi@eacn 
street is 60 feet, and that the width ac and ad of each road- 






a, lop) 


f 
1 


=| 
| 
| 
| 





ma 





A Re cana 
Pa 
St SS ea eer eee 
| Fata Peete eee rs 
aA ae . | 
D 
FIG. 422. 


way is 40 feet; also, that the grades of the street descend at 
the rate of 2 per cent. for A Band's per cent. tore — ee 
the directions indicated by the arrows. The grade lines of 
both streets must, of course, have the same elevation at 9, the 
intersection of the center lines. As computed by the grade 
of A 4, the elevation of the curbing would be, at the points 
a and d, the amount .02 x 20 = 0.40 of a foot above the in- 
tersection 0, and at the points c and 6 the same amount 
below it. As computed by the grade of C D, however, the 
elevation of the curbing at a and ¢ would be .05 x 20= 
1.00 of a foot above the intersection 0, and at d and 0 it 
would be the same amount below it. Consequently, we 


STREETS AND HIGHWAYS. 1073 


obtain the following elevations, with reference to the inter- 
section o, for the curbing at the points a, c, d, and J, desig- 
nating elevations above by the + sign and elevations below 
by the — sign: 

On Grade of On Grade of Difference 


Curb-Angle. A B. GJ). in Feet. 
a +. .40 + 1.00 0.60 
C — .40 + 1.00 1.40 
a + .40 — 1.00 1.40 
b — .40 — 1.00 0.60 


In the last column is given the difference between the 
elevations of each curb angle, as determined from the two 
different grades. It is evident, however, that each angle of 
the curbing can have but one elevation; how to harmoni- 
ously adjust these diverse conditions is a problem that is in 
some cases quite difficult of solution, and one concerning 
which quite different views are held. Some of the methods 
employed wiil now be noticed. 


METHODS OF ADJUSTMENT. 

1739. Method by Adjustment at Curb Angles.— 
When the grades of the intersecting streets are quite flat, 
so that the difference in the elevations of the curb angle, as 
determined from the two grade lines, is quite small, the 
curbing of each street may be carried at the street grade 
through the entire block to the property line of the inter- 
secting street, and the adjustment of the elevations of the 
curbing be made between the points where the curbings in- 
tersect the property lines. Thus, on the portion 4 of the 
street A B, Fig. 422, the curbs may be set to the regular 
street grade as far as the points c, and J, on the property 
line of the intersecting street C Y); and on the portion C of 
the street C ) the curbs may be placed at the regular street 
grade as far as the points @, and c, on the property line 
of the street A B. The elevations of the curbing at the 
points c, and c, being thus fixed at the grades of the respect- 
ive streets, the elevation of the curb angle may be deter- 
mined by giving the curb a uniform grade between the 


1074 STREETS AND: HIGH Waayis: 


points c, andc,. More satisfactory results will generally be 
obtained, however, by making the elevation of the curb 
angle a mean between its different elevations as gtven by the 
grade lines of the two streets; the elevation of the curb 
angle will here be determined in this manner for this method 
of adjustment. This method of adjustment, however, will 
not be satisfactory where the grade of either intersecting 
street is at all steep. . 


1740. Method by Independent Curb Grades.—A 
better method of adjusting the elevations of the curbing, 
where the grade of each street continues uniform to the 
center of intersection, is to set the curbs at independent 
grades through the block from curb angle to curb angle. 
Having determined the elevations of the curb angles at the 
two adjacent corners of a block, by calculating for each its 
elevation according to the grade of each intersecting street, 
and taking the mean of the results, as in the preceding 
method, the grade of the curbing is made uniform through 
the block from curb angle to curb angle, provided there is 
no change in the rate of the street grade along the block 
between the curb angles. (If the rate of the street grade 
changes at one or more points along the block between the 
curb angles at its adjacent corners, the grade of the curb- 
ing should be made uniform from the elevation fixed for 
each curb angle to the elevation of the street grade at the 
nearest change. In some cases, it may be found advisable 
to fix the elevations of the curb angles somewhat above or 
below the mean of the elevations calculated from the two 
street grades; this will not be done here; however. ~ (ius; 
referring to Fig. 422, the curbing would be set at a uniform 
gerade from the curb angle a to the curb angle at the left- 
hand corner of the same block, corresponding to the curb 
angle c of the adjacent block, provided there was no change 
in the street grade between those points. 


1741. Method by Level Intersections.—Another 
method of harmonizing the grades at street intersections is 
to make the grade of each street level across the intersect- 


STREETS AND HIGHWAYS. 1075 


ing street, either from property line to property line, or 
from curb line to curb line. The total amount of rise or 
fall necessary to each street between any two successive 
intersecting streets will be effected wholly along the block 
between the property lines of the block, or between the curb 
lines of the two intersecting streets, as the case may be. 

If the rise or fall is effected wholly between the property 
lines of the block, then, at the property line of each inter- 
secting street, the grade changes to a level grade and con- 
tinues level across the full width of the street. At the 
points 0,, 0, 0g, and o,, Fig. 422, where the center line of 
each street crosses the property lines of the intersecting 
street, the grade lines have the same elevation as at the 
center of intersection o. The elevation of the curb will 
require no special adjustment; at every cross-section of the 
street it will be the same as that of the street grade directly 
Opposite. “At the points 2, @,, and ¢., ¢, ¢c;, and-<¢,, etc., the 
curbs will have the same elevation as the points @,, 0 
and as the center of intersection a. 

The results will generally be more satisfactory if the 
changes of grade for each street are made at the curb lines 
of the intersecting street. This will give a slightly greater 
distance in which to attain the necessary rise and fall be- 
tween two adjacent streets, and, consequently, a slightly 
easier grade, and will allow the grade of the curb to con- 
tinue uniform to the curb angle, giving a somewhat better 
appearance. Only that portion of the intersection included 
between the curb lines is made level. This level portion of 
the intersection will be the rectangle having its four angles 
at the curb corners a, c, @, and 0, Fig. 422; at these points, 
the tops of the curbs will have the same elevation as the 
Genter of intersection... 

By the method of level intersections, the problem of 
harmonizing the system of grades is put in the simplest pos- 
sible aspect. On this account, it is a quite popular method 
and is much employed. On steep grades, however, it has 
the disadvantage of giving two abrupt changes in the grade 
line at every street intersection. Moreover, in ascending 


Sai Fat <4 8 aie 


1076 STREETS AND. HIGHWA Ys: 


such a grade, the level intersections will have the appear- 
ance of descending in the opposite direction. ‘This may be 
to some extent corrected by the following modification of 
the method. 


1742. Modification of the Method of Level In- 
tersections; Laterally Sloping Roadway.—Where 
two streets intersect, it is not commonly the case that both 
streets have steep grades. If theyintersect upon a hillside, 
it will usually be the case that one street will have the same 
general direction as the slope and that its grade will be cor- 
respondingly steep, while the other street will have a direc- 
tion across the slope or along the side hill, with a compara- 
tively level grade. It will generally be advantageous tothe 





residences and lawns along the latter, or side-hill street, as 
well as to the street intersections, to give the surface of this 
street a lateral slope in the direction of the general slope of 
the natural surface. With a sloping crown, this can be 
done by simply throwing the summit of the crown towards 
the upper side of the roadway. A somewhat similar effect 
can of course be accomplished in other ways, but this 
method will be the only one noticed here. 


1743. Eccentric Crowns.—The form of cross-section 
is shown in Fig. 423; it will here be called an eccentric 





a 
a’ x ee 
y 7 = YY) YY yy Uj ZY Y YY 
YYW ]/ Yj 7 | // 


crown. With the crown in this position, if the same uni- 
form slopes are retained for the sides of the roadway, the 
top of the curbing a’, on the side nearer the summit of 
the crown, will be higher than that of the curbing 0’, on 
the opposite side, by the amount d, as shown in the figure. 
If the street A 5, Fig. 422, be given a cross-section of the 
form shown in Fig. 423, the curb angles a and d and the 
curb angles ¢ and 6 of the former figure will correspond, 
respectively, to the curbs a’ and 0’ of the latter figure, and 











FIG. 423. 


STREETS AND HIGHWAYS. 1077 


the street CD, Fig. 422, may have the rate of grade = 


(ae 
(Fig. 423) across the street A 2, while in all other respects 
the intersection may be treated as a level intersection. The 
changes of grade should preferably be made at the curb. 
lines. 

The expedient of modifying the level intersection by giv- 
ing a lateral slope to the roadway of the street extending 
along the side hill can often be employed to good advan- 
tage. No adjustment of the grades of the curbs will be 
required, except, merely, such adjustment of the eleva- 
tions of the curbing on the side-hill street as may be neces- 
sary to give the proper lateral slope to the street. The 
grade of this side-hill street, to which is given the lateral 
slope, should be level across the intersection. On the in- 
tersecting street, that is, on the street extending up and 
down the hill, the elevation of the curbing will then be the 
same as that of the street grade in the same cross-section. 


1744. Formulas for Eccentric Crowns.—The 
cross-section of the roadway shown by a somewhat exagger- 


ated outline in Fig. 424 is the regular form of cross-section 





Fic. 424. 


with sloping crown, except that the summit o of the crown, 
instead of being at the center m of the roadway, is at the 
distance ¢ from the center and nearer the higher curb a’. 
This distance ¢ will here be called the eccentricity of the 
crown. For a cross-section having an eccentric crown, the 
length of the central curve joining the uniformly sloping 
portions of the surface line and the rate of slope on the 
latter should remain the same as though the crown were 
symmetrical; the rate of slope should be as given by for- 
mula 207. This being the case, the amount of eccentricity 


1078 STREETS AND HIGHWAYS. 


of the crown necessary to give the desired difference be- 
tween the elevations of the curbs will be given by the 
formula 


a 
4 aes .-oe" 
ee 


(211.) 


in which e is the eccentricity of the crown and d is the 
difference in the elevations of the curbs, both in feet, while 
s is the rate of slope as obtained by formula 207. 

The height of both curbs above the gutters or adjacent 
surface of the roadway should generally be made equal to 
_the height of crown as given by formula 205, and as sub- 
stituted in formula 207, to obtain the value of s. If both 
curbs have this height above the gutter, and the eccentric- 
ity of the crown be as given by formula 211, then the ele- 
vation of the summit of the crown will be a mean between 
the elevations of the two curbs. In other words, the top of 


. wes : a . 
the higher curb a’ will be at the distance 5 above the summit 


of the crown, and that of the lower curb 0’ will be at the 
same distance below it. Although the rate of slope will re- 
main unchanged, the amount of crown will really be some- 
what less in an eccentric than in a symmetrical crown. 

Formula 211, for the eccentricity of the crown, does not 
apply correctly when d, the difference between the eleva- 
tions of the curbs, is greater than the value-of 2. 
by the formula 


d, = s (w — b), (212.) 


in which s is the rate of slope, zv is the width of the road- 
way, and @ is the width of the curved portion of the crown, 
as in formula 207 3 d,, 1s the maximum difference between 
the elevations of the curbs to which formula 211 will 
correctly apply. 


as given 


1745. Roadway with Uniform Lateral Slope.— 
When d has a value greater than that of d,,, as determined 
by applying formula 212, the crown should be omitted, and 
the roadway surface should be given a uniform slope from 
curb to curb, as shown in Fig. 425. For a cross-section of 


STREETS AND HIGHWAYS. 1079 


this form, the elevation of the highest point in the surface 
line of the roadway, or the point a,, Fig. 425, should gen- 
erally correspond to the elevation of grade. The rate per 
foot s, of uniform slope across the roadway, or the amount 


i 


$$$ 
FIG. 425. 


of vertical fall in each horizontal foot, will be given by the 
formula 


: 
| 
| 
| 
| 
| 
| 
| 
| 


x WH 
ULLLLLELY. 
SJ 


J, Eee (213.) 


in which d is the difference in the elevations of the curbs, 
and w is the width of the roadway, as shown in Fig. 425. 
The rate of slope s,, as given by this formula, will generally 
be somewhat less than the rate of slope s, as given by for- 
mula 207 and used in formula 212. The height of each 
curb above the adjacent surface of the roadway may be made 
equal to the amount of theoretical crown c substituted in 
formula 2Q7 to obtain the value of s. The curbs may have 
any desired height above the surface of the roadway, how- 
ever, so long as both curbs have the same height. 


1746. Exampeie.—For the roadway of Example (4) of Art. 
1728, (2) how much eccentricity must be given to the crown in order 
to elevate the top of one curb .48 of a foot above the top of the lower 
curb? (4) If the difference in the elevations of the curbs be .72 of a 
foot, will the formula for eccentricity apply correctly ? (c) With this 
difference between the elevations of the curbs, if the surface of the 
roadway be given a uniform slope from curb to curb, what will be the 
rate of slope 5; ? 





SoLUTION.—(a) In the solution of the example referred to, the rate 
of slope s in the uniformly sloping portion of the cross-section was 
found to be .016; the difference d in the elevations of the curbs, as 
stated above, is .48 of a foot. By substituting these values in formula 
211, the necessary amount of eccentricity for the crown is found to 
be equal to . 


A8 
2X .016 
(6) The width of the roadway is 48 feet, and the width of the central 
curved portion is 5 feet (Art. 1728). By substituting in formule 


= 15 feet. Ans. 


1080 STREETS AND HIGHWAYS. 


212, we have dm = .016 (48 — 5) = .688 of a foot. The difference of 
.72 of a foot between the elevations of the curbs is greater than this 
value of dm; hence, for this difference, the formula for eccentricity 
will not apply correctly. Ans. 

(c) By applying formula 213, the rate of uniform slope across the 


v9 
roadway 5s, is found to be Se aaa) Leer yN S17 


EXAMPLES FOR PRACTICE. 


Note.—The following examples relate to those of Art. 1728 in 
which sloping crowns were assumed. To the roadways of those ex. 
amples, which are now, for convenience, assumed to have level grades, 
the formulas for laterally sloping roadways will be applied. 

1. For Example 2, the width of roadway is 20 feet and the height of 
crown is .44 of a foot. (a) What will be the value of @,, for this road- 
way? (6) If one curb be elevated .55 of a foot above the other, -will 
the formula for eccentricity of crown apply correctly? (¢) How much 
eccentricity of crown will be necessary to give this difference in the 

pert ake bale 
heights of the curbs? ae § (a) .66 ft. 

(cy) Oo Fe. 

2. The width of roadway and height of crown for Example 3 are 
60 feet and .555 of a foot, respectively. (a) What will be the value of 
@»m for this roadway ? (6) With a difference of one foot between the 
heights of the curbs, will the formula for eccentricity of crown apply 
correctly ? (c) How much eccentricity of crown will be necessary to 


give this difference in the heights of the curbs ? ‘Aine { (2) 1.02 tC 
“U(c) 2 ft. 


3. For Example 5, the width of the roadway is 24 feet and the height 
of the crown is .415 of a foot. (@) What will be the value of @,, for this 
roadway? (4) If the top of one curb be placed .75 of a foot above the 
top of the other curb, will the formula for eccentricity of crown apply 
correctly ? (c) If the roadway surface be given a uniform slope from 
curb to curb, what will be the rate of slope ? Ans § (a) .664 ft. 

U(c) .08125 ft. 

4. For Example 6, the width of the roadway is 36 feet and the 
height of the crown is .386 of a foot. (a) With a difference of .50 of a 
foot between the elevations of the tops of the curbs, will the formula 
for eccentricity of crown apply correctly ? (46) How much eccentricity 
of crown will be necessary to give this difference in the elevations of the 
curbs ? Ansis (0) Leak tte 


1747. Elevations of Block Corners.—The angles 
of the property line, ge, 2 and we Big 422 ate caue 
block corners. With reference to the street A £4, the 


STREETS AND HIGHWAYS. 1081 


block corner c’ is opposite the point c, of the curbing where 
it crosses the property line of the street C ); but with ref- 
erence to the street C D, the same block corner c’ is opposite 
the point c, where the curbing crosses the property line of 
the street A &. In the case of an intersection level between 
property lines, the curbs will have the same elevation at the 
points ¢, and c¢,, in which case the elevation of the block 
corner c’ will be the same as computed by the lateral slope 
of each sidewalk in the manner noticed in Art. 1736. If 
the intersection is not level, however, the curbs will not 
have the same elevation at the points c,and c,. In any 
case, the elevation of the block corner will be given by the 
formula 
BOS, +e,+ Se (zw, + w,). (214.) 

in which c’ is the elevation of the block corner, c, and c, are 
the respective elevations of the two curbs at points opposite 
the block corner (see Fig. 422), w, and w, are the widths in 
feet between the block corner and the respective curbs (the 
widths c’c,andc’c,, Fig. 422), and s, is the lateral slope per 
foot between the curb and the building line, which is here 
taken at a value of .02 (see Art. 1736). 


1748. Exampie.—The curb cc, Fig. 422, is at a distance of 12 
feet from the block line a’ c’, and has a grade of 2 per cent., descending 
from c; the curb ¢c. isat a distance of 10 feet from the block line 0’ c’, 
and has a grade of 5 per cent., ascending from c. If the curb angle c 
has an elevation of 102.48, what should be the elevation of the block 
corner ¢'? 

SoLuTION.—The elevation of the curb at ¢c, will be 102.48 — .02 x 
10 = 102.28, and the elevation of the curb at c, will be 102.48 +.05 & 12 = 
103.08. By applying formula 214, the elevation of the block corner 
102.28 + 103.08 2 .02 & (12 + 10) SANGO ke A ne: 





c’ is found to be 


EXAMPLES FOR PRACTICE. 


Note.—The following examples refer to Fig. 422. 


1. The curb aa, hasa grade of 2 per cent., ascending from a, and 
the distance aa, is 10 feet; the curb aa, has a grade of 5 per cent., 
ascending from a, and the distance aa, is 12 feet. If the elevation of 


io AY ts 


1082 STREETS AND HIGHWAYS. 


the curb angle a is 102.48, what should be the elevation of the block 
coriera Ans. 103.10. 


2. The curb dd, has a grade of 2.10 per cent., ascending from ad, and 
the distance dd, is 8 feet; the curb dd, has a grade of 4.85 per cent., 
descending from d@, and the distance @d@, is 12 feet. If the elevation of 
the curb angle d@ is 102.48, what should be the elevation of the block 
corner @'? Ans. 102.473. 


3. The curbangle 4, which has an elevation of 102.48, is at a distance 


pret 


of 11 feet from the property line 64’ c’ and at a distance of 15 feet from 
the property line 6’d'. The curbs 64, and 6d, have grades of 2.20 and 
5.24 per cent., respectively, both descending from 4. What should be 
the elevation of the block corner 0’? Ans. 102.226. 


4. The distance cc, is 15 feet, and the curb has a grade of 6.84 per 
cent., descending from c; the distance cc, is 12 feet, and the curb has 
a grade of 1.25 per cent., ascending from c. If the curb angle ¢ has an 
elevation of 87.42, what should be the elevation of the block corner c’ ? 

Ans. 87.252. 


1749. Drainage at Intersections; Location of 
Catch-Basins.—In order that vehicles may pass smoothly 
over street intersections, the crown of each roadway should 
be continuous across the intersection; the crown of either 
roadway should not be 
broken by the gutters 
of the inters éc time 
street. It is: ¢vident 
however, that some 
provision must be made 
for the storm water 
from the gutters on the 
upper side” Giwemaa 
crown. 

Each of the inter- 
secting streets shown 
in Fig. 426 is assumed 
to have a descending 
grade in the direction 
indicated by the arrows marked along its center line, and 
the crown of each street is assumed to be continuous. With 
such grades, the storm water from the gutter c, can flow 
around the curb angle c into the gutter c,, as indicated by 





STREETS AND HIGHWAYS. 1083 


the curved arrow, and, likewise, the storm water from the 
gutter 7, can flow around the curb angle @ and find an out- 
let in the gutter d,. The storm water from the vicinity of 
the curb angle J can flow away in either gutter 0, or 6,.. In 
both of the gutters @, and a,, however, the storm water 
flows towards the curb angle a, and, as there is no gutter 
leading away from this curb angle across the crown of either 
roadway, some provision must be made for the storm water 
from these gutters. 

If a storm-water sewer extend along either of the inter- 
secting streets, the problem of providing for the storm water 
at the curb angle a may be easily solved by simply putting 
a catch-basin at the curb angle, as indicated by the dotted 
circle. The storm water from the gutters a, and a, would 
be received directly into the catch-basin, from which it would 
be conveyed into the sewer. Catch-basins would also gen- 
erally be placed at the curb angles c and d to receive the 
storm water from the gutters c, and d@,, so that the gutters 
c, and d, would not be overcrowded. It is evident that a 
catch-basin would not be required at the curb angle 0. 

If there be no storm-water sewer along either of the inter- 
secting streets, so that the storm water must be conveyed 
wholly by the surface gutters, it will be necessary to provide 
a conduit leading from the gutter at the curb corner towards 
which the water from both streets flows, corresponding to 
the curb angle a, Fig. 422, across and beneath the roadway, 
discharging into the descending gutter, as the gutter c, or 
d,, atsome point far enough down to give the required depth 
below the roadway surface. In some cases, it may be ad- 
visible to provide such a conduit under each roadway. 


MATTERS RELATING TO GRADES. 


ESTABLISHING GRADES. 
1750. Objects to Be Attained.—lIt is usually quite 
difficult to properly decide all the various matters that must 
be considered in fixing the grades for a system of streets, and 
adjusting them so as to harmonize at intersections, The 


1084 STREETS AND HIGHWAY s: 


three main objects to be attained are: first, the prompt 
removal of the surface water; second, the easiest gradients, 
and third, the good appearance of the street. 


1751. Removal of Surface Water.—In order that the 
surface water may be promptly and effectually removed from 
a roadway, the rate of grade for the street should never be 
less than one-fourth of one per cent., that is, .25 of a foot 
per 100 feet; the grade should not be as flat as this except 
in extreme cases and with first-class pavements, such as 
brick or asphalt. A minimum grade of one-half of one per 
cent. is as flat as should generally be used, and a grade as 
steep as one per cent. 1s very désirable. . Where the oradqe 
line of a street has the same elevation at the intersecting 
streets at both ends of a block, instead of making the grade 
level through the block, it should be elevated in the center 
of the block sufficiently to cause the water to flow in each 
direction towards the intersecting streets. If the street is 
sewered, the grade may be depressed at the center oierne 
block by locating catch-basins there; it will, however, gen- 
erally be better tolevate the grade at the centers mae 
block. 


1752. Easiest Obtainable Gradients.—This will be 
governed largely by the character and slope of the natural 
surface,.and the nature and extent of the improvements 
that have been made along the street... Where no improve- 
ments have been made, quite deep cuts and fills are per- 
missible in order to obtain favorable grades. But where 
buildings have been erected and improvements of a per- 
manent nature have been made along a street before the 
grade is established, as is frequently the case, due regard 
must be given to such improvements in fixing the grade. 
The engineer must simply study the conditions as he finds 
them, and work out the most favorable grade possible to 
those conditions. | 

This will seldom be as satisfactory a grade as could have 
been established before the improvements had been made, 
but it should be as free from abrupt changes and approach 


STREETS AND HIGHWAYS. 1085 


as near toa uniform grade between street intersections as 
possible, thus giving the easiest obtainable gradients. It 
is important that the grade of a street be established as 
soon as possible after the street is laid out and before im- 
provements are made; the improvements should then con- 
form to the established grade. 


1753. Good Appearance of Street.—Although the 
matter of appearance has been placed last, it is by nomeans 
the least in importance. The general appearance of a 
street greatly affects the value of the adjacent property; it 
is, consequently, of great importance that the grade of a 
street be such as to give it a good appearance. Where 
possible, the grade of the street and the curb line should ex- 
tend unbroken through each block from curb angle to curb 
angle. When it is necessary to change the grade at some 
point along the block, the change should be made at a prop- 
erty line, and should be as small in amount as _ possible. 
Where the necessary change in the grade is considerable, 
the total change should be accomplished by means of several 
small, uniform changes, approximating a vertical curve, 
rather than by one abrupt change. 

If residences have been built along the street before the 
grade is established, as is not infrequently the case, some 
regard should be had for the appearance of the lawns in fix- 
ing the grade; the appearance of a@a// the lawns should be 
considered in the aggregate, however, rather than the 
appearance of any particular lawn. The appearance of the 
street intersections must also be considered. In short, the 
appearance of the entire system of grades, as a whole, must 
be carefully considered, for it is their effect as a whole, and 
not the effect of any particular detail, that will be noticed. 


1754. General Methods of Procedure.—As stated 
above, it is usually quite difficult properly to decide all the 
various matters that must be considered in fixing and 
harmonizing the grades for a system of streets. There is 
no established custom among municipal engineers with 
regard to this, and the practice varies materially. Indeed, 


STREETS AND HIGHWAYS. 


1086 








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STREETS AND HIGHWAYS. eLOST 


some engineers prefer not to follow the same rule with 
regard to any two streets, but in each case to establish such 
a grade and harmonize it with that of each intersecting 
street in such manner as the conditions of that particular 
case may seem to demand. This is probably a better prac- 
tice than to attempt to follow any rigid rule, for a method 
that would be satisfactory in one case would be likely to 
prove unsatisfactory in another. 

In general, it is a good plan to fix first the grades of the 
streets extending in one direction, choosing the direction of 
the more important streets and taking them in the order of 
their importance; then fit in the grades of the cross streets, 
taking them also in the order of their importance. In fit- 
ting in the grades of the latter streets, it will often be 
found advisabie to modify the grades of the former more or 
less. If the system of streets is extensive, a contour map 
will often be of value as an aid in fixing the grades. When 
the street grades have been finally fixed, the grades of the 
curbs should be harmonized at the intersections in the man- 
ner that may be best suited to each case. 


GRADE RECORD. 

1755. Records of Grades.—A complete and system- 
atic record of all grades should be preserved in a book kept 
for that purpose, and generally known as a grade record. 
For each street upon which a grade is established, this 
record should give the rates of grade along the different 
portions of the street, with the elevation of each station, 
or, at least, of each street intersection and point where the 
grade changes. The information given should fully describe 
the grade of the roadway and of each curb. This record 
should be supplemented by a complete and accurate profile 
of the street. All information should be so well indexed as 
to be easily and quickly accessible. 

The book in which the records of the grade are kept 
should be made especially for that purpose, with pages so 
ruled as to be convenient for recording the grades. The 
best form for this record book will depend somewhat upon 


1088 STREETS AND HIGHWAYS. 


the engineer’s ideas and methods in recording the grades. 
For most cases, the accompanying form of page will be found 
satisfactory. The notes given are merely for the purpose 
of illustrating the method of recording the grade. It will 
be noticed that, in recording the rate of grade, a rising 
grade is indicated by a-+ sign, and a falling grade is in- 
dicated by a — sign; a rate of 0.0 is given for a level grade. 
In order that each station or plus where the grade changes 
may be easily distinguished, it is designated by a X marked 
in the column for the rate of grade. 


CITY BASE AND BENCH MARKS. 

1756. The City Base.—All elevations relating to the 
grades, and to all other matters of municipal improvement, 
should be referred to, and measured from, the elevation of 
a point on some permanent object in the municipality, of 
which the elevation is known from a record, or to which a 
certain elevation is assigned; the elevation of the point, 
whether assigned arbitrarily or otherwise determined, is 
permanently fixed and recorded. The elevation of this 
point will be its distance above an imaginary horizontal 
plane adopted as the zero elevation for all levels. This 
plane of zero elevation is usually called the city datum, 
city base, or, simply, the base. It is a great advantage 
for all the levels of a municipality to be referred to the same 
base. The elevations of any points in the municipality can 
then be readily compared by simply determining and com- 
paring their elevations above base. Moreover, if the eleva- 
tions of certain fixed points of reference are determined and 
recorded, with regard to the base, the elevations of any 
points on a grade line, as recorded, can easily be obtained 
from these and fixed upon the ground. 


1757. Bench Marks.—A point whose elevation is 
determined and recorded for reference is called a bench 
mark. For the levels of a municipality, it is customary to 
fix, arbitrarily or by comparison with some object whose 
elevation is known, the elevation of one point as the princi- 
pal and governing point of reference; this is called the 


STREETS AND HIGHWAYS. 1089 


primary bench mark. From this, a system of aux- 
iliary bench marks, or secondary bench marks, 
should be extended throughout the municipality. The ele- 
vation of the primary bench mark, when once fixed, remains 
unchanged as the final point of reference for all levels ; the 
elevations of all other points, including the system of sec- 
ondary bench marks, are obtained from, and referred to, 
the elevation of the primary bench mark. The elevations 
of the secondary bench marks, however, depending upon 
the accuracy of the levels by which they are established, are, 
of course, subject to correction in case any error is dis- 
covered. 

In cities near the seashore, the elevation of mean tide is 
not uncommonly taken as the city base; from this base, the 
exact elevation of some fixed and permanent point is estab- 
lished as a primary bench mark. For inland cities, how- 
ever, the base is commonly taken simply at some multiple 
of 100 feet below the permanent point chosen for the pri- 
mary bench mark. 


MARKING AND PERPETUATING THE STREET 
LINES AND PROPERTY LINES. 
NECESSITY FOR MONUMENTS. 

1758. The Obliteration of Lines.—In most cities, 
it is very difficult to accurately locate the positions of the 
street and property lines. In many cities, there are streets 
whose lines can not by any possible means be accurately and 
certainly located in the positions where they were originally 
established. The stakes and monuments that originally 
marked the lines, and which have not uncommonly been of 
a temporary nature, become decayed, removed, and destroyed 
during the development of the city. As the result of care- 
lessness and indifference, it is often the case that no effort 
is made to preserve the markings of the lines, and they 
become more or less obliterated, and, in some cases, wholly 
obliterated. It is the experience of all cities that much 
trouble and annoyance, and often serious litigation, is caused 
by the obliteration of lines and boundaries. 


1090 STREETS AND HIGHWAYS. 


The destruction of the original markings of the lines would 
not be a very serious matter if the buildings and fences were 
built exactly along the property lines so as to accurately 
mark their positions. This is not always, or even usually, 
the case, however. It appears to be the natural instinct of 
property owners to attempt to get possession of as much 
of the adjacent land as possible; the land properly belong- 
ing to the street is generally considered as common plunder. 
The buildings and fences first erected are not uncommonly 
found to encroach upon the adjacent property; both build- 
ings and fences very commonly encroach upon the street. 
The lines of existing fences and buildings can not be de- 
pended upon as the bases of measurements to establish other 
lines, except in cases where they are positively known to be 
COLrec’ ‘ 

1759. How to Mark the Lines.—In order that the 
true positions of the street and property lines may be accu- 
rately determined at any time, they should be permanently 
marked by durable monuments set deep into the ground; 
the positions of the monuments should be determined and 
fixed by measurements to other permanent objects, and the 
descriptions and positions of the monuments and the objects 
to which the measurements are taken, with the measure- 
ments, should be recorded. The importance of establishing 
and recording a sufficient number of such monuments to 
definitely describe and perpetuate the positions of all street 
and property lines can scarcely be overestimated. Much 
trouble and annoyance, and more or less expensive litigation, 
will be saved thereby. | 

The monuments should be established at all important 
street intersections. If the street lines or block lines areso 
marked as to be readily determined, the internal property 
lines of the block can generally be easily determined from 
the block lines. To establish monuments that would per- 
manently define the positions of the street lines would ap- 
pear to be a simple matter, but it is found to involve very 
serious difficulties. te 


STREETS AND HIGHWAYS. 1091 


POSITIONS OF MONUMENTS. 

1760. Positions Commonly Adopted.—Where to 
place the monuments for street lines so that they will escape 
destruction during the progress of municipalimprovements 
is a question that has never been satisfactorily answered. 
Three different general positions adopted for the street 
monuments in different cities, and advocated by different 
engineers, are: at the intersections of the center lines of 
the streets, at the block corners, and on arbitrary lines at 
some certain uniform distance from the block lines. 


1761. Monuments on Center Lines.—The most 
convenient and, in many respects, the most satisfactory 
position for the monuments is at the intersections of the 
center lines of the streets. Most engineers favor this posi- 
tion. Monuments set well into the ground and entirely 
below the surface along the center lines of the streets will 
génerally remain convenient and reliable as points of refer- 
ence until sewers are constructed on the streets. As the 
sewers are usually located along the centers of the streets, 
monuments set on the center lines are generally destroyed in 
the excavation of the sewer trenches. The monuments may 
also be destroyed by excavations made for other purposes. 
If not set deep, they may be destroyed by excavations made 
in constructing street-railway tracks. 


1762. Monuments on Block Lines.—Monuments 
set at the block corners are also convenient for determining 
the lines. They will be safe from being destroyed by ex- 
cavations made in the street, but will almost surely be 
obliterated in the construction of buildings or fences along 
the block lines. The corner of the building, or the corner 
post of the fence, will always be said to be placed ‘‘ exactly 
where the stake was”’; if the width of the street is measured 
between two such corners, however, it will generally be 
found to be somewhat narrower than it should be. The 
corner of a fence or building can not be depended upon to 
indicate the location of the true corner, unless its position 
with reference to the true corner is positively known. The 


1092 STREETS AND HIGHWAYS. 


block corners are even less satisfactory positions for the 
monuments than the intersections of the center lines of the 
Streets. 


1763. Monumentson Offset Lines.—In order that 
the monuments marking the block lines may not be destroyed 
in the construction of fences and buildings, they are some- 
times placed on arbitrary offset lines located in the streets 
at some convenient and 













yf) 

_ uniform distance from 

V///, the block line. ‘This is 
_ the 


WY fy 

i _ 
yy 
V7 illustrated in Fig. 427, 


none nnanng f nnn pmmennnnnm—nm—- 1 Which are shown the 
block lines and the offset 
lines at the intersection 
| oftwo streets. The full 
| 
i 






lines are the block lines, 
m and the angles 0 are the 


i a Ge ee  — — +} 0 


S| 
= 









WY, «Dlock corners; the small 
YYygg circles m represent the 


Y 


_ monuments, and the 
L dotted lines are merely 

BIGg ce: the arbitrary offset lines 
on which the monuments are set. These offset lines are 
usually at some uniform distance from the block lines, which 
offset distance must be shown on the records. 

The minimum offset distance employed for this purpose 
is usually about 1.5 feet, and the maximum 1s about 4 feet. 
In other words, the monuments are usually set at some uni- 
form distance of from 1.5 to 4 feet from the block corners, 
measured perpendicularly from the block line. On residence 
streets, such positions are generally quite satisfactory for 
the monuments. An offset distance of 1.5 or 2 feet will 
usually bring the monuments between the block line and the 
sidewalk, while a distance of 3 or 4 feet will generally bring 
them under the sidewalk; in either of these positions, the 
monuments are not usually likely to be disturbed, so long 
as the street remains a residence street. On business streets, 















SS Q 
a a en eo a 





STREETS AND HIGHWAYS. 1093 


however, monuments placed in any such positions will 
generally be destroyed in constructing the buildings. In 
most business blocks, the basements of the buildings are ex- 
tended beneath the sidewalks, as vaults for the storage of 
fuel, etc. In excavating for these vaults, any monuments 
set in the street near the block line will be certain to be 
destroyed. Such positions for the monuments are satisfac- 
tory only on residence streets where no excavations are made 
beneath the sidewalks. 


MATERIAL FOR STREET MONUMENTS. 


1764. Requirements for a Satisfactory Monu- 
ment.—There is considerable difference of opinion with 
regard to what forms the most satisfactory monument for 
marking street lines. The monument should be easily dis- 
tinguishable and should be of as permanent a nature as pos- 
sible. It should be of durable material and should be set 
deep in the ground in such manner as not to be easily dis- 
turbed. It is also desirable that it be so arranged that, if 
the upper portion be disturbed or destroyed, the lower por- 
tion will still remain to indicate its position. Many differ- 
ent kinds of monuments are used, from wooden stakes to 
cut-stone posts. It will be well to notice briefly some of 
the different materials commonly used for street monuments. 


1765. Wooden Stakes.—In the greater portion of 
the Government land surveys, the corners are marked with 
wooden stakes. In ordinary land surveys and in the sur- 
veys of village plots, wooden stakes are also extensively 
employed to mark the corners. Such stakes will soon 
decay, and though they form much more durable marks 
than is generally supposed, they can scarcely be considered 
to be permanent monuments. If a wooden stake is driven 
into soil of light character, the form of the stake will remain 
distinctly discernible as long as the soil remains undisturbed, 
though the stake itself be wholly decayed. The exact space 
occupied by the stake will be filled with the dark mold re- 
sulting from its decay, and this will be easily distinguish- 


1094 STREETS AND HIGHWAYS. 


able in light colored soil of a sandy nature. ‘This fact has 
been of great value in re-establishing the corners of the 
Government land surveys. While wooden stakes have well 
served their purpose in these surveys and are satisfactory 
for temporarily marking survey lines, they are not suitable 
for permanently marking street lines in a city. 


1766. Iron Stakes.—Corners are often marked by 
iron stakes. These commonly consist of pieces of gas-pipe 
or of ordinary round wrought-iron bars about three-quarters 
of an inch in diameter; they are generally supposed to be 
more permanent than wooden stakes. They possess one 
peculiar advantage; when there is no other iron near, the 
position of an iron stake will be indicated by the movement 
of the needle of a compass when held near to the ground in 
the immediate vicinity of the stake, thus enabling the stake 
to be quickly found. Such iron stakes will rust away ina 
comparatively few years, however, and they are, therefore, 
not very satisfactory as monuments for the lines and cor- 
ners of surveys. Larger stakes would, of course, last longer 
before rusting out, and it should also be noticed that cast 
iron will resist rust much better than wrought iron. 


1767. Brick Monuments.—For some _ purposes, 
reasonably satisractory monuments may be made by boring 
into the ground with an ordinary post auger about four 
inches in diameter, and placing bricks end upon end in the 
hole thus formed, then filling around the bricks with pul- 
verized rock, coal, charcoal, brick, lime, or other indestruct- 
ible material easily distinguishable from the surrounding 
soil. One advantage of brick monuments is that the re- 
moval of the upper bricks will not disturb those below. 
Such monuments, however, though reasonably satisfactory 
for the corners of land surveys in the country, are not well 
adapted to marking the lines of city streets. 


1768. Monuments of Pulverized Material.— 
Similar to the brick monuments are those formed wholly of 
indestructible pulverized material. They are formed in 
the same manner as the brick monuments, except that the 


STREETS AND HIGHWAYS. 1095 


bricks are omitted, and are adapted to about the same 
purposes. 


1769. Fireclay Monuments.—Solid cylinders of 
vitrified fireclay, of suitable length and diameter, make 
quite satisfactory corner monuments. Such cylinders or 
corner posts, 4 inches in diameter and 2 feet long, are manu- 
factured by the Jackson Fireclay Company, of Jackson, 
Mich., who, so far as we know, are the only manufacturers 
of such monuments. These monuments can be set in a 
hole made by a 4-inch post auger; they should be set with 
their tops nearly a foot below the surface. 


1770. Monuments of Cement.—A monument that 
is probably more satisfactory than any of the preceding can 
be formed by boring into the ground with a post auger, as 
for the three preceding kinds of monuments, and filling the 
hole with mortar composed of one part hydraulic cement to 
about two parts clean, coarse sand. A cross X can be 
marked in the top of the monument to indicate the exact 
position of the corner orline. When the mortar has become 
set, it will form a very substantial and durable monument. 


1771. Stone Monuments.—Probably the best monu- 
ments for marking the positions of lines and corners are 
those composed of very large stones. The stone for a street 
monument should be somewhat of the general form of a 
pyramid or prism, and not less than about 3 feet in length; 
it should be set with the larger end downwards. The 
smaller end of the stone should be so dressed as to forma 
suitable top for the monument that would be easily recog- 
nized; the exact position of the corner should be indicated 
by a X or other suitable mark. It is unnecessary that any 
other portion of the stone should be dressed, as it will be 
buried deep in the ground out of sight. Monuments com- 
posed of large, heavy stones are not easily removed, 
destroyed, or even disturbed; they are, generally, the most 
permanent and satisfactory monuments for marking lines 
and corners. 


1096 STREETS AND HIGHWAYS. 


SETTING, WITNESSING, AND RECORDING MONUMENTS. 


1772. Manner of Setting Monuments.—Monu- 
ments should be set so deep in the ground as not to be easily 
disturbed. In setting them, the earth should be well packed 
around them, so that there will be no danger of them set- 
tlinge out-of position. “1f (set in) the roadway .etnossno.. 
should be from about six inches to a foot below the surface, 
according to circumstances. If set in a paved street, an 
opening to the top of each monument should be left in the 
pavement; the opening should be covered by a casting 
similar to the cover of a sewer manhole, though smaller. 
When monuments are set under the sidewalk, their tops 
may be just beneath the sidewalk, with an opening through 
the sidewalk protected by a casting, or the tops of the 
monuments may be flush with the surface of the sidewalk. 
When the monuments are set on the block line, or between 
the biock line and the sidewalk, they may project somewhat 
above the surface of the ground, if desired. The monu- 
ments should be set in such manner as to be easily accessible 
and, at the same time, not easily disturbed. 


1773. Witnessing Monuments. — Although the 
monuments should always be of a permanent nature, they 
are likely to become destroyed, removed, or disturbed in the 
improvements attending the development of a municipality. 
Their positions should therefore be thoroughly fixed and 
identified by measurements to other permanent objects, so 
that, if disturbed, they can be replaced in their original 
positions. Moreover, such measurements enable the monu- 
ments to be easily found when beneath the surface of the 
ground, and to be positively identified when found. As the 
objects to which measurements are taken will also be liable 
to become destroyed or removed, measurements should be 
taken to a sufficient number, so that, if some are destroyed, 
the position of the monument can still be determined from 
those that remain. If there are not a sufficient number of 
permanent objects in the vicinity, reference monuments 
may be set to which measurements can be taken. These 
should project above the ground, so as to be easily seen. 


STREETS AND HIGHWAYS. 1097 


The practice of identifying the positions of monuments 
marking the lines and corners of surveys by means of 
measurements to other permanent objects is called witness- 
ing the monuments. It is a simple and effective method of 
identifying the positions of monuments, and is very com- 
mon among surveyors. The objects to which the measure- 
ments are taken are called witnesses, witmess trees, 
witness monuments, etc. 


1774. Restoring Monuments. —If a monument 
that has been well witnessed is destroyed or removed in the 
construction of improvements, it will generally be possible 
to replace the monument in its original position after the 
improvements have been completed. The monument should 
not be replaced, however, until after the ground has become 
thoroughly settled; if replaced before, it is liable to settle 
out of position. It is to be borne in mind that it is not the 
monument itself, but its posztzon, that is of value. 


41775. Records of Monuments.—Accurate records 
should be kept of the positions of all monuments marking 
lines and corners. All measurements witnessing the posi- 
tions of monuments, with descriptions of the monuments 
and witnesses, should be recorded. Each monument and 
its position with reference to the street lines should be 
described, and all witness measurements identifying its 
position should be given, with descriptions of the witnesses 
to which the measurements are taken. The records of 
monuments fixing the positions of street lines, and of the 
witnesses identifying their positions, should be copied into 
a book kept for the purpose, and should be so indexed that 
the record of any desired monument can be easily found. 





ENCROACHMENT OF LINES; STATUTES OF 
LIMITATION. 

1776. Encroachment of Lines.—In connection 
with the subject of marking and perpetuating the street and 
property lines, it will be well to notice the subject of en- 
croachment, as relating to the acquisition of title by adverse 


T. IV.—19 


1098 STREETS AND HIGHWAYS. 


possession. This is a matter which must in all cases be 
settled either by mutual agreement between the parties 
interested, or by the courts; but it is well for the municipal 
surveyor to understand his proper position in relation to it. 

That fences and buildings are not always upon the true 
property lines, but very commonly encroach upon the street 
or upon the adjacent private property, is a fact well known 
to all experienced surveyors. Most surveyors also under- 
stand that lines of such fences and buildings may, under the 
usual conditions and after the lapse of sufficient time, 
become the legal boundaries of the property. 


1777. Statutes of Limitation.—In order to placea 
limit upon the continuance of litigations and disputes over 
property lines, the laws of the different States decree to the 
effect that apparent and undisputed possession to any fence 
or building line for a certain period of time (which period of 
time varies in different States) will establish such lines as 
the legal boundaries of the property. Such laws are called 
statutes of limitation, and the occupancy of property by 
which title is gained under the statute of limitation is 
commonly known as adverse possession. 


1778. Duties of the Surveyor with Regard to 
Encroachments.—lIt should be clearly understood by the 
municipal surveyor that he has nothing whatever to do with 
the legal boundaries of property established by the statutes 
of limitation. Such lines do not in any way affect the 
positions of other lines. They are wot survey lines and can 
not be taken as the basis of any surveys or measurements 
relating to the establishment of other property lines, except 
in cases where subsequent deeds may specially mention them 
as the basis of the description in a conveyance of property. 
With this exception, the only lines which the surveyor has 
to deal with are the true lines of the original survey. 
These are the only lines for him to run or to survey from. If 
any particular boundary line or portion of a boundary line 
becomes legally established in any position other than on the 
true line of the property as originally laid out, that is a 


STREETS AND HIGHWAYS. 1099 


matter to be determined by the courts; the services of the 
surveyor are manifestly unnecessary in such a case, as his 
work would merely show that the line was not in its original 
position. After the line has been established by the courts, 
the surveyor may be called upon tc mark and describe its 
position. Such a line, however, in no way affects the work 
of the municipal surveyor in determining the positions of 
other lines; its position may become the legally established 
boundary for that particular line and property, but it does 
not affect the.position of any other boundary line. 





BAR i leN Ge. 


TRACTION. 


RESISTANCE TO TRACTION. 


1779. Asan introduction to the study of pavements, 
it is necessary to consider the resistance to traction as weil 
as the tractive power of horses. The total resistance to 
traction may be said to be composed of three distinct re- 
sistances, namely: axle friction, rolling resistance, 
and grade resistance. For the present purpose, the 
resistance of the air may be neglected. 


1780. Axle friction depends entirely upon the 
nature and lubrication of the bearing surface of the axle 
and upon the magnitude of the load, being directly propor- 
tional to the latter. The effect of this resistance is constant 
and usually small, and may be neglected. 


1781. Rolling resistance relates to the resistance 
which the roadway surface offers to the wheels of vehicles 
rolling upon it. It may be subdivided into two classes, 
-namely: Ist, the resistance due to small obstacles in the 
roadway or inequalities in the roadway surface; 2d, the re- 
sistance of a wheel rolling upon a smooth surface, which 
resistance is called rolling friction. 


1782. Resistance Due to an Obstacle.—This is 
measured by the horizontal force necessary, when applied 
at the axle, to raise the load upon the wheel to the height of 
the obstacle. In Fig. 428 the tractive force ¢, and the load 
qw are both applied upon the axle a. From the theory of 
moments it is known that, in order that the tractive force 
¢~, may be sufficient to balance the wheel, supporting the 


For notice of copyright, see page immediately following the title page. 


1102 PAVING. 


weight w upon the obstacle 0, the moment of the force ¢, 
acting upon the lever arm y must be 
equal to the moment of the force w 
acting upon the lever arm +, or, to ex- 
¢ press it algebraically, 74, y= w +, from 
which 


Sarai em ged AOD (215.) 


a J 7 —0 


iG. 428. being the radius of the wheel and 
o the height of the obstacle. The value of 7,, as given by 
this formula, measures the resistance of the obstacle, and 
any tractive force greater than 7, will pull the wheel over 
the obstacle. For small obstacles, this resistance may be 
considered to be inversely proportional to the square root 
of the diameter of the wheel. It should be noticed, how- 
ever, that the resistance of small obstacles and inequalities 
in the roadway surface is due largely to the shock produced 
by them, and is greater at high than at low speeds. 


1783. Rolling friction is due chiefly to the com- 
pressibility of the roadway surface, which permits the wheel 
to somewhat compress or indent it. It 
is sometimes called resistance to 
penetration. When the wheel of a 
vehicle is drawn upon a roadway sur- 
face it will indent it and produce in it 
a wave that is forced along ahead of the zy 
wheel, as indicated in Fig. 429. The | 
wheel is thus always climbing a slight FIG. 429. 
inclination, or, more correctly, and what amounts to about 
the same thing, is constantly compressing new material. 

This resistance is less for large than for small wheels, but 
the ratio by which it varies has never been definitely deter- 
mined. Some experiments that have been made indicate 
that the resistance is approximately inversely proportional 
to the diameter; other experiments indicate that it is ap- 
proximately inversely proportional to the square root of the 
diameter; while, from mathematical investigation, it has 





PAVING. 1103 


been concluded that, for wheels rolling upon roadways of 
homogeneous material, the resistance to traction is inversely 
proportional to the cube root of the diameter. It is probable 
that the last conclusion is the most nearly correct. If this 
is the case, then the resistance of a wheel of a certain diam- 
eter will be to that of a wheel of one-half the diameter as 
1 . 
V1 WB 
difference. As the variation in sizes of the wheels on 
ordinary road vehicles is not very great, this condition may 
generally be neglected, and for practical purposes the re- 
sistance may be taken equal to the load multiplied by a co- 
efficient depending upon the nature and condition of the 
roadway surface. 





or as 1: 1.26 (nearly), which is not a very great 


1784. Tractive Resistance on Various Surfaces. 
—Numerous experiments have been made to determine the 
tractive force necessary to haul a given load upon various 
roadway surfaces. The results vary through a wide range, 
as is to be expected when the many different conditions that 
may affect the results are taken into consideration. The 
table of Resistance to Traction, given in Tables and For- 
mulas, is compiled from different sources and is believed 
fairly to represent the results of the experiments that have 
been made; it gives the approximate maximum, minimum, 
and mean tractive forces, in pounds, required to haul a load 
of one gross ton (2,240 pounds) at an ordinary pace, on level 
roadway surfaces of the kinds named, and also the mean 
tractive force in fractional parts of the load. Itisto be 
understood that these values are but rough approximations. 

The frictional resistance to traction on a level roadway is 
given by the general formula 

i= OW, (216.) 
in which ¢ is the tractive force necessary to overcome the 
rolling resistance, zw is the load, and c is the value given in 
the last column of the table for the various kinds of roadway 
surfaces. The constant c is called the coefficient of 
rolling friction. 


1104 PAVING. 


1785. Grade Resistance.—In ascending inclines a 
very great part of the tractive force is expended in over- 
coming the resistance of gravity due to the incline, which 
is equal to the load multiplied by the total rise and divided 
by the length of the incline; in other words, it is equal to 
the load multiplied by the sine of the angle made by the 
incline with a horizontal line. 





Fic. 430. 


Fig. 430 represents a wheel on an inclined plane B C, 
whose inclination to the horizontal is the angle Ad C B= x. 
The weight on the axlec is w, represented graphically by 
the line c 6. According to the principle of the parallelogram 
of forces (Art. 884), the weight «w may be resolved into 
the two forcesca = w,andcd=t,, the former perpendicular, 
thelatter parallel-to B.C. ~ The anegles*2 @Geanda vente 
each equal to A C 4, on account of having their sides per- 
pendicular to the sides of A CB. Also, ca=— 67a, as these 
two lines are opposite sides of the parallelogram ca 0d. 
The components 7, and w, are easily found by solving the 
right-angled triangle c 0 d, as follows (see Art. 754): 


bie 0 OS ee ee (217.) 
1) Ui COO Sain = ale sete (218.) 


The force ¢/, is the resistance due to the inclination of the 
surface 4 C, and is independent of the friction. In order to 


PAVUNG 1105 


find the resistance due to friction, we apply the following 
general principle: | . 

The friction between two surfaces ts directly opposed to the 
direction of motion, and equals the normal, or perpendicular, 
pressure between the two surfaces multiplied by the coefficient 
of friction. (See Art. 1784.) 

In the present case, the pressure between the two surfaces 
is w,. Therefore, the frictional resistance offered by the 
wheel is 

PE a= 2 7e COs oe (219.) 

If 7 is the total tractive force necessary to just pull the 

wheel up the plane, we must have 
f= te 4 fF w (sitet - ¢.cos-7),* (220.) 

If we wish to prevent the wheel from rolling down the 
plane, we reason thus: The direct force pulling the wheel 
down is 7,; but in this case the frictional resistance ¢, opposes 
the downward motion; the resultant force 7, acting down 
the plane, and the one that is necessary to apply in an 
opposite direction, to keep the wheel from moving down- 
wards, is, therefore, 


T,=t,—t, = w (sin r—c cos +). (221.) 
If we put the total rise Ad =f, the inclined length 


BC =i, and the horizontal length A C =—J,; the values of 


Z,, w,, and ¢, become: 


wp wp 
{= = md (222.) 
l; V¥PPt+l,? 


wl, w L, d, 








Li = a SX (223.) 
l; Vp’ +4, P 
sa aR EL ya AR alld Sa I. (224.) 
; ; rT ey p 


from which corresponding values can be written for 7 and 7\. 


* The force 7’ is really only sufficient to balance the resistances; in 
order that there may be motion, the tractive force must exceed 7. 
But, as any excess of the tractive force over 7, no matter how small, 
will produce motion, we usually say that 7 is the force necessary to 
pull the load up the plane. 


1106 PAVING. 


1786. Approximate Formulas.—Where the incli- 
nation is small, we may write, approximately, /; = /,, whence 





Pi ere x lie W == UW) 1 == 6 We compat ce tori 
216). The quantity f represents the rate of rise per unit 
h 


of (horizontal) length. The rate per 100. or per cent-‘is 
evidently 100 xX f Calling 7, the rate per unit, and 7,,, the 
h 


rate per cent., there results: 


ee (225) 
h 
reno oe (226.) 
h 
Pree ates 
f=r=78 (227.) 


Therefore, we have the following expressions for the value 
8) 8 (3e 
he os T 100 
Lae : 100° 





i= w 


(228.) 


rh Easy pi Bar ota 
Alison eerie es (; +¢) 13h; (Fs +<). (229.) 


1787. Angle of Repose.—In descending a grade, the 
component ¢, becomes an accelerating force, and it may be 
necessary to apply a holding-back force 7, (formula 221), 
in order to keep the vehicle from ‘‘running away.” It is 
evident, from formula 221, that this will be the case when- 
ever ¢, is greater than /,, that is, when the component of the 
weight along the plane is greater than the resistance due to 
friction. If ¢, is greater than 7,, the force 7, will be nega- 
tive, which means that the vehicle will have to be pulled 
down the incline, no holding-back, or brake, force being 
necessary. It may happen that the resistance of friction 
is just enough to keep the wheels from rolling down, 
in: which case’ 7. = 7. and, therefore, from. formulas 2 © ae 


Sits t; er aCOSete 


PAVING. 1107 


In this case the angle + (Fig. 430) is called the angle of 
repose; it is the angle just beyond which the resistance of 
friction is no longer sufficient to keep the body from sliding 
or rolling. This angle, of course, varies with the nature 
both of the surface of the incline and of the rolling body. 
A general expression for it may be found from the preceding 
equation; for, if we callit x,, we have (see Fig. 430) 

2 


Sitiat et COS st a= 


th 
“he e,’ 


and the equation referred to becomes 
l 
js rs 


whence (Art. 754), 


Pine ; batt, (230.) 
h 

Therefore, the angle of repose ts the angle whose tangent 
ts equal to the coefficient of friction. If the coefficient of 
friction is known, we look in a table of natural tangents for 


the angle whose tangent is that coefficient, and that will be 


the required angle of repose. Since hee Riana srees 100 7-., 


Ly 
it also follows that the per cent. of grade giving the angle 
of repose is 
Zz < 
To eer Ue (23 15) 
u 
1788. Examp.e (a).—What will be the tractive force required 
to draw a wheel 5 feet in diameter, supporting a load of 400 pounds, 
over an obstacle 6 inches (=.5 foot) in height resting upon a level 
roadway surface ? 
SoLuTION.—The radius of the wheel will be one-half the diameter, 
or 2.5 feet. By formula 215, the tractive force 7/, will be equal to 


400 x 4/(5 — .5) X.5 
35 —.5 





= 300 pounds. Ans. 


EXAMPLE (6).—What will be the total tractive force required to haul 
a load of 5,000 pounds upon an ordinary macadam roadway having an 
ascending grade of 4 per cent. ? 


1108 PAVING. 


SoLuTIoN.—As obtained from the table of Resistance to Traction, 
the value of c for ordinary macadam roadways is 3; =.04. By formula 
229, 7=5,000 (45 + .04) = 400 pounds. Ans. 

EXAMPLE (c).—What will be the rate per cent. of grade giving the 
angle of repose for an ordinary Belgian-block pavement ? 


SoLuTION.—From the table, the value of c for an ordinary Belgian- 
block pavement is 7, = .025. By substituting this value of cin formula 
231, we get “100 = 100 x .025 = 2.5 per cent. Ans. 


EXAMPLES FOR PRACTICE. 


1. What will be the total tractive force required to haul a load of 
6,400 pounds upon a roadway paved with asphalt and having an as- 
cending grade of 2%? Ans. 192 lb. 

2. What will be the total tractive force required to haul a load of 
3 gross tons upon a roadway paved with good granite blocks, and 
having an ascending grade of 5 per cent.? Ans. 504 Ib. 


3. What will be the rate per cent. of grade that will give the angle 


of repose for a roadway paved with ordinary granite block ? 
Ans. 4.00%. 


4. What will be the total tractive force required to haul a load of 
4,800 pounds upon a hard-rolled gravel roadway having a grade of 
3 per cent.? Ans. 304 lb. 


5. What will be the rate per cent. of grade giving the angle of 
repose of an asphalt pavement ? Ans. 1.002. 


6. What will be the total tractive force required to haul a load of 


2 gross tons upon an ordinary earth roadway having a grade of 104 ? 
Ans. 855 Ib. 


7. What will be the tractive force required to draw a wheel 4 feet 
in diameter, supporting a load of 200 pounds, over an obstacle .4 of a 
foot in height, resting upon a level roadway surface ? Ans. 150 Ib. 


THE TRACTIVE POWER OF HORSES. 


1789. General Statement.—The loads that a horse 
can pull upon any given roadway surface will not necessarily 
be proportional to the resistance to traction offered by the 
surface, but will depend upon the strength of the animal, 
its training, its familiarity with the roadway surface, and its 
ability to obtain a foothold upon it. Owing to the differ- 
ence in strength, speed, and training, the work that can be 
performed by different animals varies greatly, and it is pos- 





PAVING. 1109 


sible to make only a roughly approximate statement with 
regard to the average amount of work that a horse can do. 


1790. Average Work of a Horse.—The tractive 
power of a horse diminishes as the speed increases. Within 
moderate limits of speed, say from three-fourths of a mile 
to four miles per hour, the tractive force that can be exerted 
by a horse is nearly inversely proportional to the speed; the 
amount of work performed may, therefore, be considered 
constant. It is considered that a good average horse, 
weighing 1,200 pounds and traveling at a speed of 2.5 miles 
per hour, or 220 feet per minute, can exert, on a smooth, 
level road a pull or tractive force of 100 pounds, which is 
equivalent to 100 K 220 = 22,000 foot-pounds of work per 
minute. This represents the work of a rather superior 
horse, however, and it will probably be more correct to 
assume that the average horse, working regularly 10 hours 
a day, can exert a tractive force of 90 pounds when travel- 
ing on an ordinary level roadway at a speed of 2.5 miles per 
hour. This is equivalent to 90 * 220 = 19,800, or say 20,000 
foot-pounds of work per minute. This value will here be 
used. Hence, for moderate speeds, the average tractive 
force that can be exerted by a horse will be given by the 


formula 


) 
nae ee (232.) 


in which /’ is the average tractive force in pounds and s’ is 
the speed in feet per minute. 

If the tractive force #’ is known, the average speed s’ at 
which a certain load can be transported may also be com- 
puted from formula 232. 

As there are 5,280 feet in a mile and 60 minutes in an 
hour, speed expressed in miles per hour can be reduced to 
feet per minute by multiplying by 5,280 and dividing by 60, 


oP ae PaO, 20U) 
or by multiplying by the fraction — == 88: 


1791. Maximum Work and Tractive Force ofa 
Horse.—The work done by a horse is greatest when he 


1110 PAVING. 


moves at a speed of about one-eighth the greatest speed 
with which he can move when drawing no load; this will be 
called the speed of greatest work. The force exerted 
at this speed is about 0.45 of the utmost tractive force that 
the animal can exert at a dead pull. From this it may be 
seen that a horse can exert for a short time a tractive force 
of about double that which he can exert continuously, so 
that much heavier loads can be hauled over steep short 
grades than over the same grades if long. Hereafter, in 
problems, the maximum tractive force of a horse at a dead 
pull will be taken at just double the average tractive force, 
as given by formula 232. 


1792. Examp te (a).—What will be the tractive force that can 
be exerted by an ordinary horse at a speed of 4 miles per hour ? 


SoLutTion.—A speed of 4 miles per hour is equal to AIS 





352 feet per minute. Hence, by formula 232, the tractive force that 
20,000 
352 





can be exerted by an ordinary horse at such a speed will be 
57 pounds (nearly). Ans. 


EXAMPLE (4).—If, for the conditions described in Example (4) of 
Art. 1788, the load is drawn by two horses, what will be the average 
speed ? 

SoLuTion.—If the total tractive force of 400 pounds is exerted by two 


horses, then each horse will exert a tractive force of sa = 200 pounds, 


2 
20,000 


300 = 100 feet per minute. Ans. 





and the average speed will be 


EXAMPLES FOR PRACTICE. 


1. At what average speed will two horses haul the load of Example 1, 


ACtedi2 O82 Ans. 208.3 ft. per min. 
2. What will be the average speed at which two horses can haul 
the load of Example 2, Art. 1788? Ans. 79.4 ft. per min. 


3. How many horses will be required to haul, at a speed of 200 feet 
per minute, a load of 8,000 pounds upon a roadway paved with good 
granite block and having a grade of 2.50 per cent. ? Ans. 4 horses. 

4. How many horses will be required to haul a load of 8,000 pounds 
at a speed of 200 feet per minute upon a roadway paved with asphalt 
and having a grade of 1.50 per cent. ? Ans. 2 horses. 


PAVING. HERI 


PAVEMENTS. 


GENERAL CONSIDERATIONS. 

1793. Object of Pavements.—Pavements are con- 
structed for the purpose of improving the facilities for, and 
reducing the cost of, transportation, and for increasing the 
safety, speed, and comfort of travel. The office of a pave- 
ment is to furnish an impervious covering that will protect 
the soil of the natural foundation, and distribute the con- 
centrated weight of the loads more evenly upon it, at the 
same time affording a smooth, even surface that will offer 
the least possible resistance to traction, and over which 
vehicles may pass with ease and safety. 


1794. Qualities Essential to Pavements.—A good 
pavement should be: 

Ist. Impervious, in order not to retain water or surface 
liquids, but to facilitate their discharge into the side 
gutters. 

2d. Such as to afford asecure foothold for horses, and not 
to become polished and slippery from use. 

3d. Hard, tough, and durable, so as to resist wear and 
disintegration. 

4th. Adapted to the grades. 

5th. Suited to the traffic. 

6th. Smooth and even, so as to offer the minimum resist- 
ance to tracticn. 

7th. Comparatively noiseless. 

8th. Such as to yield very little dust or mud. 

9th. Easily cleaned. 

10th. Economical with regard to first cost and main- 
tenance. 

It is also desirable that the pavement should be of such 
material and construction that it can be readily taken up in 
places and quickly and substantially relaid, in order to give 
access to water, gas, and sewer pipes. 


1795. Of What a Pavement Consists.—A_ pave- 
ment consists of two more or less distinct parts, namely, 


1112 PAVING. 


Ist, the wearing surface, and 2d, the foundation by which 
the wearing surface is supported. 

The wearing surface may be termed the working portion 
of the pavement; it is that visible part with which those 
who travel over it are familiar. It receives and sustains 
the traffic, and is that part of a pavement by which the 
traffic is directly affected. The first nine items of the pre- 
ceding article relate directly to the wearing surface, which 
must be of such material and so constructed that it will not 
only be best suited to the traffic but also resist its destructive 
effect in the best possible manner. 

The wearing surface, however, is properly little more than 
a surface, and is not of itseli capable of sustaining the 
traffic and distributing its weight over a sufficient area of 
the yielding soil beneath it. Hence, it is necessary that the 
wearing surface should rest upon, and be sustained by, a 
foundation having sufficient strength to resist deformation 
and to distribute the concentrated weights of the traffic 
over a sufficient area of the underlying soil, so that the lat- 
ter will sustain it without injury. In any pavement the 
value and condition of the wearing surface,and,consequently, 
the value of the pavement, will depend largely upon the 
foundation. 


1796. Different kinds of pavements are generally 
designated by the names of the materials used for their 
wearing surfaces. Prominent exceptions to this are the 
macadam and telford broken-stone pavements, which have 
practically the same wearing surfaces, but differ materially 
with regard to their foundations. These pavements are 
named after their inventors. 

_ There are and have been many varieties of pavements, of 
which the following are the ones most extensively used: 


Asphalt pavements. Wood-block pavements. 
Brick pavements. Cobblestone pavements. 
Stone-block pavements. Broken-stone pavements. 


These are named in about the order of their comparative 
merit, although the comparative merit of different pave- 


PAVING. 1113 


ments will depend greatly upon the character of the traffic 
to which they are subjected. When properly constructed 
and each kind of pavement is subjected to the character of 
traffic to which it is adapted, most of these pavements have 
proved fairly satisfactory. 

Each kind named may be taken to represent a class- 
Under the name of asphalt are included not only all kinds 
of asphalt pavements, properly so called, but also all pave- 
ments composed of bituminous products, such as_ the 
pavement known as vulcanite or coal-tar distillate, etc. 
Under the name of ‘‘stone-block pavements” are included 
all pavements composed of stone shaped to any required 
form, such as the pavements known as granite block, 
Belgian block, etc. The name ‘‘wood-block pavements” 
includes all wood pavements, while by ‘‘cobblestone pave- 
ments’ is meant all pavements composed of natural stone, 
unshaped and unbroken. 


CHOICE OF PAVEMENTS. 


1797. Factors Involved.—The selection of the pave- 
ment most suitable to a given roadway will depend greatly 
upon the local circumstances attending each particular case. 
The suitability of the pavement should be considered with 
reference to each of the following conditions: Ist, adapta- 
bility; 2d, serviceability, including safety; 3d, durability, 
and 4th, economy. It will be well here to notice each of 
these conditions separately, although they are more or less 
dependent upon one another. 


1798. Adaptability.—The pavement upon a road- 
way should be adapted to the class of traffic that will pass 
over it. The pavement suited to the roadway of a suburban 
district would not be suited to the roadway of a manufact- 
uring center, and the pavement suitable for a residence 
street would not be well adapted to the requirements of a 
street sustaining very heavy traffic. In general, it may be 
stated that for important commercial thoroughfares 





iL ae 


1114 PAVING. 


sustaining heavy and constant traffic, granite-block pavements 
are suitable; asphalt, brick, and wooden-block pavements 
are well adapted to the requirements of streets in localities 
where noise is very undesirable, such as important residence 
streets and streets devoted to retail trade; while, for pleasure 
drives and suburban streets having lhght traffic, broken-stone 
pavements are suitable. 


1799. Serviceability.—The serviceability of a pave- 
ment, or its fitness for use, may be measured by the expense 
caused to the traffic using it, that is, the fatigue of horses, 
wear and tear of vehicles, loss of time, etc. It will depend 
to some extent upon the foothold that it affords to horses. 
The rougher the surface of the pavement, the more secure 
will be the foothold afforded, while at the same time the 
greater will be the resistance to traction. Cobblestone 
pavement affords an excellent foothold, but offers great 
resistance to traction and causes much wear and tear of 
vehicles and fatigue of horses. Asphalt pavement affords a 
less secure foothold for horses than almost all other kinds of 
pavements, but it also offers less resistance to traction and 
causes less wear and tear of vehicles and fatigue of horses. 
The best measure of these conditions is the expense to the 
traffic using the pavement. For this purpose, however, no 
statistics are available. The cost of wear and tear on differ- 
ent pavements has been roughly estimated to be as given in 


the following table: 
TABLE 36. 


Estimated Cost of Wear and Tear on Different Pavements, 
in Cents per Mile Traveled. 


On -cobblestone*pavemente.. 7 es eee a ee 5.0 
On Beloian-block- pavement vn she eee 4.0 
On*granite-bl6ck pavements 1. a ae eee eee 3.0 
Oniwood pavement aren sian ate eee eee 2.5 
On first-class broken-stone pavement............... 1.2 
On“asphalt*pavement?.a eee eee eke O 


1800. Safety.—The consideration of safety is properly 
included in that of serviceability. The comparison of 
different pavements with regard to safety is commonly 


PAVING. 1115 


based upon the average distance traveled by a horse before 
it falls, this distance representing the comparative security 
of foothold offered by the pavement. The comparative 
security of foothold afforded to horses by roadway surfaces 
of different materials, stated in the order of their safety, is 
as follows: 


1..Earth (dry and compact). 
2. Gravel. 

3. Broken stone. 

4, Wood. 

5. Sandstone and brick. 

6. Asphalt. 

”%. Granite block. 


Statistics also indicate the following conditions with 
regard to the safety of three very common pavements, 
namely, asphalt, wood, and granite: 

Asphalt and wood are most slippery when merely damp, 
and safest when perfectly dry; they are also safest when 
clean. Asphalt requires but little moisture to become very 
slippery; it is in its most slippery condition when the dry 
weather comes after rain. 

Wood requires more rain than asphalt before reaching its 
most slippery condition, but the slippery condition lasts 
longer. A small quantity of dirt on asphalt makes it very 
slippery. Asphalt is usually dry and safe in winter during 
frost, while wood, retaining moisture, is very slippery. 
Under snow, however, there is very little difference. 

Slipperiness may be prevented on asphalt by sprinkling it 
with sand, and on wood by sprinkling it with gravel. More 
or less dirt and dust will, of course, result from this. The 
tendency of the sand will be to wear out the asphalt, while 
the tendency of gravel will be to preserve the wood. 

Granite is most slippery when dry and _ safest when 
thoroughly wet; it is also less safe when clean. In damp 
weather the granite blocks become greasy and slippery. 
The blocks always become more or less rounded by the 
traffic, and, in dry weather, if the granite is of a hard, close- 
grained variety, their surfaces will become polished and 


very slippery. 


1116 : PAVING. 





1801. Durability.—The durability of a pavement is 
that property that relates to the length of time that it is 
able satisfactorily to sustain the traffic, that is, to the length 
of time that it remains serviceable. This will not neces- 
sarily be as long a time as the pavement remains in use nor 
as long as the actual durability of the materials composing 
it. The pavement will remain serviceable only as long as 
its surface remains in proper condition. The best measure 
of the durability of a pavement is the amount of traffic, 
estimated as tonnage, that it will sustain before it gets in 
such bad condition that the current expense to the traffic 
from using it, in excess of the expense that would be incurred 
from using a perfect pavement, will be greater than the 
interest on the cost of renewing it. 

The durability of a pavement will depend to a great ex- 
tent upon the condition in which it is maintained, especially 
with reference to cleanliness. A covering of dirt about an 
inch in thickness will protect a pavement from abrasion and 
greatly prolong its life. The covering of dirt, however, is 
very unsanitary and otherwise objectionable; in wet weather 
it produces mud, and in dry weather, dust. 


1802. Life of Pavements.—The period of durability 
of a pavement is commonly spoken of as the life of the 
pavement. The life of different pavements under like con- 
ditions of traffic and maintenance may be taken as given in 


the following table: 
TABLE 37. 


Comparative Life in Years of Different Pavements. 














Min. Max. | Mean. 











Granite <bl6Ocksne. ye ae ee ee 12 30 21 


Asphaltign £4 5A See wah Neen ear te 10 14 12 
Brick’. ey Peas eee ae a eee 5 15 10 
Sandstone: DlOCR neuter ioe ee eee 6 12 9 
WG Od LR ete Fa ee aioe ea ees eae ae 3 7 5 
TAIMESTONG eat ee ene ae oes eres 1 3 2 








BAN eat . 1117 


The figures in this table probably represent fair values 
of the comparative durability of the different pavements 
under like conditions, but they do not represent the 
greatest endurance of the different pavements under 
the most favorable conditions. In London, pavement 
of Aberdeen granite has endured for 85 years, and 
asphalt pavement for 19 years, on streets having very 
heavy traffic. It is stated that, in the Netherlands, brick 
pavements laid half a century ago are still in good con- 
dition, and in this country there are brick pavements 
from 10 to 18 years old that are still in good condi- 
tion. The life of wood pavements has been from 5} to 
19 years in London, and in Chicago from 3 to 10 years. 
In this connection, it should be noticed that the life of 
pavements in London under very severe conditions of 
traffic is generally considerably greater than in Jarge cities 
of this country. This is probably due to greater care in 
their construction and maintenance. 


1803. Economy.—The actual economy of a pavement 
relates not only to its first cost, but also to the cost of main- 
tenance, cost of repairs to vehicles, and fatigue of horses, 
together with the facility for transportation, saving of time, 
and ease and comfort of travel afforded by its use. The 
pavement that costs the least is not always, nor even 
generally, the most economical, nor is the pavement that 
costs the most always the best. The most economical 
pavement, in a true sense, is the one that is the most 
beneficial and profitable in proportion to the cost of 
construction and maintenance. This will always be the 
pavement that is best adapted to the location and upon 
which a sufficient amount has been judiciously expended 
to secure the best results. It will cost more to con- 
struct a good pavement than to construct a poor one, but 
the well constructed pavement will last much longer, 
be more cheaply maintained, and afford much greater 
benefit to those who use it than the poorly constructed 
pavement 





1118 PAVING. 


RELATIVE ECONOMY OF PAVEMENTS. 


1804. How Compared.—The relative economic 
values of different pavements, whether of the same kind in 
different conditions, or of different kinds, may be determined 
with reasonable fairness and sufficient accuracy by compar- 
ing the average cost per ton to the traffic upon the different 
pavements for any certain uniform distance. The average 
cost per ton may be obtained by dividing the total annual 
cost consequent to the pavement by the total annual 
tonnage of the traffic upon it. The various values and 
conditions involved in this operation will now be noticed 
separately. 

1805. Total Annual Cost.—The total annual cost 
resulting from the pavement is made up of various items of 
annual expense; it may be estimated by the following 
formula: 

a=ktmtcectstd, ORF) 
in which a is the total cost, # is the first cost of the pave- 
ment, 7 is the cost of maintenance, ¢ is the cost of cleaning 
and sprinkling, s is the cost of service, and d represents the 
damages consequent to the pavement, all being accounted 
as items of annual expense. 


1806. Annual Charge for First Cost.—The first 
cost should be considered as an investment running for a 
period of time equal to the life of the pavement and having 
no value at the end of that period, except that represented 
by the permanent foundation and old materials. Conse- 
quently, the annual charge for first cost will be materially 
affected by the life of the pavement; its proper value # may 
be obtained by the formula 

Pp Seat RA ey 


i 





in which ¢, is the total first cost of the pavement, 7 is the 
annual interest on the same (which will here be computed 
at 4 per cent.), fis the final value of the foundation and 
old materials, and z is the number of years of satisfactory 


PAVING. 1119 


service, or life of the pavement. When the actual life of 
the pavement is not known, its probable life may be taken 
at the mean value given for different pavements in the last 
column of Table 37, Art. 1802. | 
The first cost of a pavement will depend greatly upon 
local conditions, and, consequently, will vary considerably 
in different localities. The cost given in Table 38 repre- 
sents fairly the costs per square yard of different pavements 
in various cities of the United States. The mean values 
given are not in all cases the average of the maximum and 
minimum values. 


TABLE 38. 


First Cost of Different Pavements, in Dollars ver 
Square Yard. 


—- 





Min. | Max. |Mean. 





aie 
—~ 


Asphalt (concrete foundation)............ 1.95 | 4.50 | 3.00 
Granite block (sand or gravel foundation) .| 1.50 | 4.25 | 2.80 
Sandstone block (sand or gravel foundation)} 1.30 | 3.00 | 2.50 


wo 


Brick (sand or gravel foundation) ........ 1.00 | 2.80 | 1.90 
Wood (sand or gravel foundation)........ .95 | 2.00 | 1.50 
Cobblestone (sand or gravel foundation)...} .40 | 1.60 | 1.00 
Separate cost of concrete foundation...... .60 | 1.50 | 1.00 











For convenience, the first cost of all pavements will be 
taken hereafter as given in the last column of this table. 
The cost of Belgian-block pavement may be taken the same 
as that of sandstone block. For stone-block, brick, or wood 
pavement on concrete foundation, 90 cents per square yard 
will be added to the cost of each, as given in the preceding 
table for sand or gravel foundation. 


1807. Final Value of Pavements.—lf the founda- 
tion of a pavement is of a permanent nature, its final value, 
that is, its value at the end of the life of the pavement, will 
gencrally not vary greatly from its first cost. <A final value 


1120 PAVING. 


of 90 cents per square yard will here be used for concrete 
foundations, while ordinary sand and gravel foundations 
will be considered to have a final value of 10 cents per square 
yard. The final value of the surface material of a pave- 
ment can be determined with a reasonable degree of accuracy 
only at the expiration of its service. Here, however, it 
will be taken as given in the following table: 


TABLE 39. 
Estimated Final Value of the Old Surface Material of 
Pavements. 
Cents per 
Sq. Yd. 

(aratiiterbloGke, anya cee 80 

Sandstone) DlOCKi. tener eee 60 

PB TIC Re ee ey ee eee ane 20 

ASON AIT or. cc) apes enanaiets Bera: 10 

WOO eons, Sica ene mee OO 


1808. Exampizr.—A roadway 30 feet wide between curbs is 
paved with granite blocks on gravel foundation. What is the annual 
charge for first cost against a piece of this pavement 10 yards in 
length ? 

SoLuTION.—A width of 30 feet is equal to = = 10 yards, giving an 
area of 10 x 10=100 square yards in the piece of pavement. From 
Table 38, the mean cost of granite-block pavement on sand or gravel 
foundation is $2.80 per square yard; as given above, the final values of 
the foundation and old surface material are 10 and 80 cents, respect- 
ively, or a total of 10+ 80=90 cents per square yard; and from 
Table 37, the mean life of granite-block pavement is 21 years. Hence, 
by formula 234, the annual charge against the pavement for first cost 


isda a = +99). 100 x .04 x 2.80 = 20.25 dollars. 
2 Ans. 





will be equal to 


1809. Annual Cost of Maintenance.—The proper 
maintenance of a pavement consists in keeping it in practi- 
cally as good a condition as when first constructed. The 
total cost of maintenance will include all outlays for repairs 
and renewals during the life of the pavement, and the 
average annual cost will be this total cost divided by the 


PAVING. 1121 


number of years of its service.. The cost of maintenance 
will depend upon the kind of pavement, quality of the 
materials used, the manner of its construction, the amount 
and character of the traffic upon it, and the condition in 
which it is kept as regards cleanliness. The estimated cost 
of maintenance should be such as would keep the pavement 
in perfect condition. The annual cost of maintenance of 
different pavements will probably average about as given in 
Table 40. These values will be used here. 


: TABLE 4oO. 
Annual Cost of Maintenance of Different Pavements. 
Cents per 


Sq. Yd. 
SGA Mi Pe Dla Krex van cin ies < he thess 2 
SANUSEONGsDIOCK 251). << ac's seems 3 
PAGE eta eret. she wb to kerp RS, oe 5 
ANC ETE | Oo NR SRR LOR Rls 2 nce iy Gy 9 
US cals OE SL. ae oF Pa oe cae Semen 15 


1810. Annual Cost of Cleaning and Sprinkling. 
—This should be the actual or estimated annual expense 
for keeping the pavement in a clean and dustless condition. 
It will depend chiefly upon the character of the material of 
which the pavement is composed and the condition of its 
surface. The actual cost of cleaning and sprinkling can be 
easily ascertained for each particular case. For con- 
venience, the costs given in Table 41, which are probably 
fair average values, will be used hereafter in all computa- 
tions. 

TABLE 41. 
Annual Cost for Cleaning and Sprinkling. 
Cents per 


Sq. Yd. 
AB METS ie rein werent dhs “arava cts stale © 2 
be kal 23 iby ine bk Rs ck geal an NAN te UR 5 
PETG PLG hear eases Wik een 10 
AT PAR Re Sahay cea t 207 Dei ogee Si 12 


1811. Annual Service Cost.—This consists of the 
various items of expense to the traffic resulting from the 


1122 PAVING: 


use of the pavement. Any loss of time or revenue caused 
by the lhmitation of speed or load below what would be 
afforded by a perfect pavement should be included under 
this head, as should also the reduced life-service of horses 
and the reduced value of their service, resulting from im- 
perfect or unsuitable pavements. The cost of wear and 
tear to the traffic using the pavement should also be in- 
cluded. (See Table 36, Art. 1799.) These various items 
should be estimated for each particular pavement, covering 
a period of one year, and their sum substituted for s in 
formula 233. The values of the different items will de- 
pend upon the kind of pavement and its condition, and 
upon the amount and character of the traffic. As statistics 
are not available, the total annual cost for service will here 
be taken as given in Table 42, in which the values are 
roughly estimated. 


TABLE 42. 
Annual Service Cost of Pavements. 


Cents per 
fab aaa 
ASDHAIUE cn ner ene 15 
Brick ees tacv hace eee 20 
WOO a ee eerie 25 
LONE DIOCK We se eee: 40 


1812. Consequent Damages.—Under this head are 
included all damages resulting from the use of defective or 
unsuitable pavements. This involves the consideration of 
many and diverse circumstances, among which may be 
named injury to health resulting from unsanitary condi- 
tions, aggravation of nervous complaints due to noise, in- 
jury to merchandise from dust and mud, reduced rental 
value of buildings due to rough, dirty, noisy, or unsanitary 
pavements, etc. Estimates of such damages will neces- 
sarily be only roughly approximate, even when made with 
care. The sum of all such items, as estimated to cover a 
period of one year, will determine the value of the quantity 


PAN UNG 1123 


din formula 233. For convenience, the values given in 
Table 43 will here be used in all estimates. It is to be dis- 
tinctly understood, however, that these values are merely 
very rough approximations. 


TABLE 43. 


Estimated Annual Damages Consequent to Pavement. 


Cents per 
Sq. Yd. 
UNS ie Ea aes fae Nee eine! so Lone 2 
VELEN ELE” oe te remo Seals eg ey 4 
ES TI CC Meee rrernes ee ee a aa an 5 
wad do Nactd 9) Cu led ao aera oor er cra 10 


1813. Summation of Annual Costs.—When the 
various items of cost, as grouped under the different heads, 
have been estimated as closely as possible, each represent- 
ing the expense due to that particular condition for a period 
of one year, then the sum of these values will represent the 
total annual expense chargeable against the pavement, as 
indicated by formula 233. It is advantageous to compute 
the total expense as annualexpense. Having obtained the 
total annual expense, however, it may be convenient, for the 
purpose of comparing with the tonnage, to reduce it to 
average daily expense, which may be done by dividing 
by 365. 

It must now be cleariy understood that the total cost 
obtained by the method just described represents the total 
annual expense (or daily expense, as the case may be) 
chargeable against a piece of pavement of certain dimen- 
sions; and it is only necessary to compare this total cost 
with the total tonnage of the traffic over the same fora 
corresponding length of time, in order to obtain the average 
cost to the traffic for transporting one ton through a dis- 
tance equal to the length of the pavement. 


1814. Examp_e.—For the pavement described in the example 
of Art. 1808, what is the total annual cost resulting from the pave- 
ment ? 


1124 PAVING, 


SoLuTion.—As determined in the example referred to, the annual 
charge for first cost is 20.25; the annual cost of maintenance is 
100 « .02 = 2.00 (Art. 1809); the annual cost for cleaning and sprink- 
ling is 100 x .10=10.00 (Art. 1810); the annual service cost is 
100 x .40 = 40.00 (Art. 1811); and the annual charge for consequent 
damages is 100 x .10 = 10.00 (Art. 1812), all results being in dollars. 
Consequently, the total annual cost a resulting from these 100 square 
yards of pavement, as given by formula 233, is equal to 20.25 + 
2.00 + 10.00 + 40.00 + 10.00 = 82.25 dollars. Ans. 


1815. Basis of Comparison.—When the total ex- 
pense chargeable against any certain piece of pavement 
has been estimated in the manner described above, for the 
purpose of comparison with other pavements, the total ton- 
nage of the traffic over the same for a corresponding length 
of time must also be estimated, in order to determine the 
cost per ton to the traffic; for a number of the items of 
expense chargeable against each pavement will be materi- 
ally affected by the amount and character of the traffic upon 
it, so that a just comparison of the relative economies of the 
different pavements will not be given by a comparison of 
their actual cost. The cost per ton to the traffic forms the 
best basis of comparison. If the total cost chargeable 
against the pavement is divided by the total tonnage of the 
traffic upon it for a corresponding length of time, the quo- 
tient will be the cost per ton to the traffic for transporta- 
tion through a distance equal to the length of the piece of 
pavement chosen. The cost thus obtained will be the cost 
per ton-mile, per ton-yard, per ton-foot, etc., according to 
the length of the piece of pavement chosen for the com- 
parison. 

It is plain that, in order to afford a just comparison, some 
uniform length of pavement must be used; for the tonnage 
traffic will be practically the same for any short distance 
along each block; that is, the number of tons of traffic 
passing over one foot of the length of a street will not vary 
materially from the number passing over one yard, one 
hundred feet, or the entire length of the block. The ton- 
nage of the traffic will be practically uniform throughout 
each block, and, in many cases, throughout several con- 


PAVING. 1125 


secutive blocks. The cost of the pavement, however, will 
be proportional to its length, and, consequently, the ton- 
nage cost will be proportional to the length of pavement 
estimated. That is, the cost per ton-yard will be three 
times the cost per ton-foot, etc. As the cost of pavements 
is generally estimated by the square yard, the ton-yard will 
be a convenient unit and will be used here. Consequently, 
the length of the pavement for which the total annual cost 
is estimated should, for convenience, be expressed in yards. 

This method of comparing the relative economy of pave- 
ments involves some error, due to the fact that the first cost 
of the pavement, and also several of the other expenses 
chargeable to it, will vary directly with its width, while the 
amount of traffic will not generally be greatly affected 
by the width of roadway, but will depend on various con- 
ditions impossible to express by formula. Moreover, the 
annual charge for first cost will be materially affected by the 
life of the pavement; the cost of maintenance will depend 
largely on the thoroughness of the construction; while both 
the service cost and consequent damages will depend largely 
on the condition in which the pavement is maintained. It 
is thus seen that there are many uncertain conditions in- 
volved; and anything approaching exactness in the results is 
not to be expected. * 


1816. Census of the Traffic Tonnage.—The ton- 
nage of the traffic over a pavement can be ascertained only 
by direct observation. As the amount of traffic is variable, 
the observations should extend over a sufficient: period to 
obtain good average results. They should be continuous 
through each day for several consecutive days and should be 
repeated at different seasons of the year. Such a series of 
observations is called a traffic census. The kind of pave- 
ment, state of repair, condition of its surface with regard to 
being clean, dry, damp, wet, or greasy, and also the number 
and kinds of partial or complete falls of horses should be 
noted when the observations are taken. 

In making the observations, the weight of each vehicle 


1126 PAVING. 


must, of course, be roughly estimated. In order for the 
observer to make an intelligent estimate, the different kinds 
of vehicles should be classified according to their approximate 
weights. The proper weight to be assigned to each class of 
vehicles may be determined by occasionally weighing a 
typical vehicle with its load. If this is done, the total ton- 
nage estimated by each day’s observation will probably not 
vary greatly from the actual total. 


1817. Classification of Tonnage.—The following 
classification has been used in making observations of 
tonnage: 

Less Tuan 1 Ton. 
One-horse carriages, empty or loaded. 
One-horse wagons, empty or lightly loaded. 
One-horse carts, empty. 


BETWEEN 1 AND 8 Towns. 


One-horse wagons, heavily loaded. 
One-horse carts, loaded. 
Two-horse wagons, empty or lightly loaded. 


OveER 3 Tons. 


Wagons and trucks drawn by two or more horses and 
heavily loaded, special note, with estimate of weight, being 
made of any unusually heavy loads, such as large trucks 
loaded with stone or iron. 


The following weights were assigned to each class of 
vehicle: 


Light-weight vehicles, including load, 4ton each. 
Medium-weight vehicles, including load, 2 tons each. 
Heavy-weight vehicles, including load, 4 tons each. 


1818. Average Daily Tonnage.—lIf the total num- 
ber of vehicles observed in each class is multiplied by the 
weight assigned to that class, the sum of the results will be 
the total tonnage during the entire period of observation. 
This sum, divided by the number of days of observation, will 
give the average daily tonnage on the roadway. If this’is 
again divided by the width of the roadway between curbs, 


PAVING. Pah ees 


in yards or feet, the quotient will be the daily tonnage per 
yard or per foot of width, which is convenient for the pur- 
pose of comparing the tonnage on different streets. For 
the purpose of ascertaining the relative economy of different 
pavements, however, it will be as well to take the tonnage 
on the full width of roadway, the cost chargeable to the 
pavement being, of course, estimated for the same width. 
If the ton-yard is taken as the unit of cost (Art. 1815), 
the traffic tonnage over one yard in length of the roadway is 
what should be observed. This will, of course, be equivalent 
to the tonnage passing any given point or cross-section of 
the roadway. If, then, the weight of each class of vehicle is 
taken as given in the preceding article, the average daily 
tonnage d@, upon the roadway will be given by the formula 


41 4+2m,+44, 
+ a 


oO 


hy 





(235.) 


in which 7, m,, and #, are the total number of vehicles 
observed in the light, medium, and heavy class, respectiv ely, 
and d, is the total number of TERE of observation. 


1819. Examp.e.—During 6 days of continuous observation, the 
number of vehicles passing over the pavement described in the ex- 
ample of Art. 1808 was found to be 3,186, classified as follows: 
1,448 light, 1,258 medium, and 480 heavy. What is the average daily 
tonnage ? 


SoLuTion.—By formula 235, the average daily tonnage ad is equal 
ee a a SO 


6 860 tons. Ans. 





1820. Statistics of Observed Tonnage.—The 
general average of the daily tonnage for certain cities of this 
country in which observations of the tonnage have been made 
was found to be 77 tons per foot of width. The average for dif- 
ferent cities varied from 151 tons in New York to 30 tons in 
Buffalo. For different streets the daily tonnage varied 
from 273 tons per foot of width on Broadway, New York, to 
7 tons on a granite-paved street in St. Louis. For all cities 
observed, the average weight of vehicles was found to be 1.15 
tons. In London, on certain streets that are paved with 


1128 PAVING. 


asphalt and on others that are paved with wood, the daily 
traffic tonnage exceeds 400 tons per foot of width, while in 
Liverpool granite-block pavements sustain a daily traffic 
tonnage of from 400 to 500 tons per foot of width. 


1821. Cost per Ton-Yard.—From what has been 
given in the preceding article may be derived the following 
formula for the value of 7¢,, the average cost to the traffic 


per ton-yard: 
a 


Jeeta hei aig 
in which a is the total annual cost chargeable against the 
pavement, as given by formula 2333 d, is the average daily 
traffic tonnage, as given by formula 235,and y is the 
length of the roadway in yards, on which the cost of the 
pavement is estimated. The value of a should be expressed 
in cents; the value of ¢, will then be in fractions of a cent. 


t (236.) 


1822. Exampie.—If the example explained in Arts. 1808, 
1814, and 1819 all relate to the same pavement, what is the aver- 
age cost per ton-yard ? 

SoLuTion.—The value of a is 82.25 dollars = 8,225 cents (Art. 1814); 
the value of d@ is 860 tons (Art. 1819); and the value of y is 10 yards 
(Art. 1808). Hence, as given by formula 236, the cost per ton-yard 


8, 225 
: = .00262 of acent. Ans. 


ty 1S equal to 365 x 860 xX 10 


EXAMPLES FOR PRACTICE. 


Norte.—In all following computations, costs and values relating to 
pavements will be taken as given in the preceding articles. In the 
following examples it will be convenient to estimate the total annual 
cost for one yard in length of roadway. 


1. Fora roadway 36 feet wide paved with asphalt, a traffic census 
extending through a period of 4 days gave the following as the total 
number of vehicles observed in each class: 1,680 light, 484 medium, and 
88 heavy vehicles. What is the average cost per ton-yard ? 

Ans. .00345 cent. 

2. For a roadway 33 feet wide, paved with brick on a concrete 
foundation, a traffic census extending through a period of 10 days gave 
the following as the total number of vehicles observed in each class: 
2,040 light, 1,506 medium, and 742 heavy vehicles. What is the average 
cost per ton-yard ? Ans. .Q0272 cent. 


PAVING. | 1129 


3. For a roadway 30 feet wide, paved with wood on ordinary sand 
foundation, a traffic census extending through a period of 8 days gave 
the following as the total number of vehicles observed in each class: 
2,112 light, 1,186 medium, and 488 heavy vehicles. What is the average 
cost per ton-yard ? Ans. .00874 cent. 


4. For a roadway 42 feet wide, paved with sandstone blocks on 
concrete foundation, a traffic census extending through a period of 
6 days gave the folfowing as the total number of vehicles observed 
in each class: 1,464 light, 1,176 medium, and 564 heavy vehicles. What 
is the average cost per ton-yard ? Ans. .00421 cent. 


PAVING MATERIALS. 


ESSENTIAL PROPERTIES AND TESTS. 


1823. Materials Employed.—The materials com- 
monly used for the wearing surface of pavements (Art. 
1795), are the following: stone in the form of blocks, 
small boulders, and broken fragments; wood in the form of 
blocks and plank; asphalt in the two forms known as 
sheet and block asphalt, and clay in the form of bricks. 
For the foundations, hydraulic-cement concrete, 
bituminous concrete, brick, broken stone, gravel, 
sand, and plank are employed. 


1824. Essential Properties of Paving Materials. 
—The properties most essential to the materials used for 
the wearing surface of pavements are: 

1st. Hardness, or the ability to resist wear by abrasion 
and attrition. 

2d. Toughness, or the ability to endure hard usage and 
withstand the destructive effect of blows. 

3d. The ability to withstand disintegration from the 
destructive effect of the weather and of the acids produced 
by decomposing organic matter. 

4th. Imperviousness to water. This property is closely 
related to the preceding. The disintegrating effect of frost 
upon materials is very great, and the less water is absorbed 
by the material, the less it will be affected by frost; con- 
sequently, the non-absorbing property is very essential toa 
satisfactory paving material, 


T. IV.—?®1 


1130 PAVING. 


1825. Rattler Test for Abrasion.—In the United 
States, what is known as the rattler test is quite commonly 
employed to indicate the ability of materials to resist abra- 
sion. Specimens of material to be tested, together with 
irregular shaped pieces of iron weighing from about 5 to 15 
pounds, are placed in a strong receptacle, such as a foundry 
tumbler, which is closed, and by means of machinery made 
to revolve a certain length of time or certain number of 
revolutions. The specimens of material and pieces of iron 
are thrown in violent collision, producing abrasion of the 
material. By this means, the relative abrasion of different 
materials may be compared. For the purpose of compari- 
son, pieces of a standard material of known quality are 
often included in the test. By weighing each specimen be- 
fore and after the test, the relative abrasion of the differ- 
ent materials may be easily determined and compared 
with the abrasion of the standard material. The rattler 
test, though of considerable value, is not entirely satis- 
factory for the purpose of indicating the non-abrasive 
qualities of paving materials, as it does not represent 
very closely the actual requirements of practical use. 
As, however, no better test has been devised, the rattler 
test is quite extensively used for this purpose. Grinding 
tests are also often used in connection with the rattler 
tests. 


1826. True Test for Abrasion.—The true test of 
paving material, however, is by experimental trial in a 
roadway under a known amount of traffic, the different 
materials being so placed as to sustain the traffic under like 
conditions. Such tests were made in St. Louis, Mo., some 
years ago. Small strips of different pavements were sub- 
jected to the repeated travel of a two-wheeled cart having 
tires 24 inches wide, the load being two tons. The amount 
of travel given the cart during the test was equivalent to a 
traffic of 50 tons per day per foot of width upon the pave- 
ment during a period of eight and one-half years. From 
the results, the number of tons traffic per foot of width on 


PAVING. | 1131 


the different pavements producing a loss of one per cent. 
was found to be as given in the following table: 


TABLE 44. 


Number of Tons Traffic per Foot of Width Producing 
a Loss of One Per Cent. on Different Pavements. 


Kind of Pavement. Tons. 
SCAN ew DOCKS es fis ct Nate eo, 70, 000.0 
Lh l aia tel Sh Maken: aie of er ea 17,200.0 
WV ON ee OOK S rat ote at Piece Oia ie ao 12, 900.0 
Pus eae ULE MOC ES net tee kt a we. o 11,100.0 
hj VaeYor 3 halal Ma) [ate ee a alee ge a 4,400.0 
hroken stone and sand... ....... 16.0 
BORE SLONG acid wale f dine win wh hos Tat 


The values given in the preceding table probably repre- 
sent quite accurately the re/atzve resistances of the different 
materials to abrasion. In these tests, however, the action 
of the elements could not be taken into consideration; under 
the ordinary conditions these would considerably increase 
the percentage of loss by abrasion. It should also be 
noticed that about one-half of the bricks were broken. 


1827. Toughness; Resistance to Crushing.—No 
satisfactory test for determining the toughness of paving 
material has been devised. Breaking and crushing tests to 
some extent indicate the toughness of the material, but they 
are not of great value for this purpose. A quick, sharp 
blow from a light hammer will probably indicate this quality 
about as well as any ordinary test that can be applied. 
This corresponds somewhat to the quick blows of the iron- 
shod hoofs of the horses upon the material when in the 
pavement. 

Resistance to crushing, however, is commonly considered 
to indicate, to some extent, the value of a material for 
paving purposes. For the most common paving materials, 
the resistance to crushing, in pounds per square inch, is given 
in Tables and Formulas (Crushing Resistance of Different 
Paving Materials); the average values given are what may 


1132 PAVING. 


be considered as about the ordinary average for the different 
materials. 


1828. Absorptive Capacity of Materials.—The 
durability of materials is much affected by their capacity to 
absorb water. The water absorbed tends to disintegrate 
the material by the expansion produced by freezing, and the 
more water the material contains, the greater will be the 
disintegration. The absorptive capacity of a material will 
depend largely upon its density. A dense material will 
absorb less water than a porous one, and, other conditions 
being equal, the less the absorption the better the material. 
Materials that have begun to decompose absorb much more 
water than perfectly sound materials. 

The relative densities of similar materials are indicated 
by their specific gravities or weights. A table of Specific 
Gravities and Absorbing Capacities of Paving Materials is 
given in Tables and Formulas. 

The weight of a material per cubic foot or per cubic 
inch may be determined by multiplying its specific gravity 
by 62.5 or .03617, respectively. 


GENERAL DESCRIPTION OF MATERIALS. 


1829. Granite.—This isan unstratified rock composed 
essentially of silica, or quartz, feldspar, and mica. Other 
minerals may also be present as accessory constituents, often 
in such quantities as to largely determine the character and 
color of the rock. 

The color of granite is produced by and varies according 
to the minerals present. If the feldspar is potash spar, it 
imparts a reddish color; if soda spar, it produces a grayish 
color. The granite will also be light or dark, according as 
the contained mica is white (muscovite) or black (biotite). 
Hornblende produces a dark mottled appearance, and 
epidote imparts a green color. 

The texture of granite varies from very fine and homoge- 
neous to very coarse, according to the minerals contained and 
the physical conditions under which they originally solidi- 


PAVING. 1133 


fied. The durability of granite depends upon its composi- 
tion and texture. Although commonly classed as the most 
durable of rocks, all granites do not possess great durability, 
and some are quite unsuitable for paving purposes. Those 
containing an excess of quartz are too brittle, those contain- 
ing an excess of feldspar disintegrate rapidly, and those 
containing an excess of mica have too laminated a structure. 

As popularly used, the term granite is applied not only to 
granites proper, but also to the similar rocks known as 
gneisses (i. e., bedded granites, syenite, and other crystalline 
rocks); it is sometimes improperly applied to trap-rocks 
also. 

The rock known as syenite is considered best for paving 
blocks. It is a massive rock, and its occurrence is like that 
of granite, but it differs from granite in containing more 
hornblende and much less quartz. 


1830. Sandstone.—These rocks are composed of 
grains of sand-held together by a cementing material. 
They are known as silicious, ferruginous, calcareous, 
or argillaceous sandstones, according as the cementing 
material is of the nature of silica, iron, lime, or clay. The 
hardness, strength, and durability of this rock, and in most 
cases its color also, depend upon the nature of the cement- 
ing material and vary greatly; if this decomposes readily, 
the mass is soon reduced to sand. The silicious and ferru- 
ginous varieties are generally durable, but the argillaceous 
and calcareous varieties of sandstone are not durable. 

Sandstones are widely distributed and represent all geo. 
logical periods. Those of the Upper Silurian and Lower 
Carboniferous formations are much used for paving ma- 
terials in the Central and Western States. These rocks are 
durable and well suited for the purpose of paving blocks, 
but do not make suitable material for broken-stone roads. 

The predominating colors are red, brown, buff, and light 
gray. A fine-grained, compact, and even-bedded sandstone 
of a dark gray color, called bluestone, is much used for 
flagging and curbing in New York and neighboring States. 


1154 PAVING, 


1831. Limestone.—This rock is essentially carbonate 
of lime, but it always contains some additional constituent 
as impurity. Limestones are said to be silicious, argil- 
laceous, ferruginous, magnesian, dolomitic, or bitu- 
minous, according as the contained impurity is silica, clay, 
iron, magnesia, dolomite, or bitumen. They may also con- 
tain other foreign mineral matter in such quantity as to give 
character to the mass. | 

The color of limestone depends upon the impurity con- 
tained; it will be white for the nearly pure carbonate. of 
lime, and may be gray, blue, yellow, red, brown, and even 
black, according to the predominating impurity. 

The texture of limestone varies greatly; it may be fine or 
coarse, sometimes resembling sandstone. Its structure, or 
the state of aggregation of its particles, also varies greatly; it 
may be dense and compact, or loosely cemented and crumbly, 
or it may be of a dull, chalky nature. Consequently, the 
hardness, strength, and durability of lmestone also vary 
greatly. Some limestones are hard and strong, and nearly 
as durable as the best sandstone; while others are so friable 
as to crumble under slight pressure, or be disintegrated 
rapidly by the action of the elements. 

Limestones are extensively used for flagging and curbing, 
and the silicious, magnesian, dolomitic, and bituminous 
varieties are eminently suitable for broken-stone roads hav- 
ing light traffic. The experience of many cities, however, 
proves that limestone is unsuitable for paving blocks. It 
wears unevenly, and in a year or two the blocks become 
split and shattered by the action of the frost. The material 
called Ligonier granite, however, which is really a sili- 
cious limestone, is very strong, and is much used for paving. 


1832. Trap-Rock.—This is the name commonly ap- 
plied to a large group of unstratified eruptive or igneous 
rocks, composed of feldspar, augite, hornblende, and some 
magnetite and titanic iron. There are many varieties of 
trap-rock, according to the proportions and conditions of 
the minerals contained. Basalt, one of the most common 


PAVING. 1135 


varieties, is of a dark green, gray, or black color. It is com- 
posed of augite and feldspar, and often contains iron; it is 
very compact in texture and quite hard. Greenstone, the 
popular name of another variety, is applied to a dark green 
rock, composed of hornblende and feldspar. Dolomite 
contains silica and feldspar, from which it receives its hard- 
ness; its color may be either light or dark. 

The trap-rocks are hard and tough, though their quality 
varies considerably in different localities. They have no 
true cleavage; consequently, they break irregularly and 
are difficult to work. The rock of the Palisades, in New 
Jersey, splits easily, however, and under the name of 
Belgian block has been extensively used for paving in 
New York city and vicinity. Since granite has come to be 
used for paving blocks, however, the trap-rocks have been 
much less used. 

The trap-rocks are exceedingly durable, and are about the 
best material for broken-stone roads. They are not really 
suitable for paving blocks, however. 


1833. Asphalit.—This is the name applied to mixtures 
of pure asphaltum with calcareous or silicious substances; 
the mixtures are both natural and artificial. Natural as- 
phalt consists of either sandstone or limestone impregnated 
with pure bitumen. These are known, respectively, as 
bituminous limestone and bituminous sandstone ; in 
general, they are called rock asphalt. The artificial as- 
phalt consists of a mechanical mixture of bitumen, sand, and 
crushed limestone. 


1834. Bituminous Sandstones.—These are found 
in Europe, where they are used chiefly for the manufacture 
of pure bitumen. They are also found in the United States, 
where they are gradually coming into quite general use asa 
paving material; they are used both in their natural state 
and mixed with other materials. 


1835. Bituminous Limestones.—These also are 
found in some parts of Europe. The limestones are usually 
impregnated with from 7 to 12 percent. of bitumen. They 


1136 PAVING. 


are employed in the production of pure. bitumen and arti- 
ficial paving materials. 


1836. Asphaltum.—This is also called bitumen, or 
mineral pitch. It is considered to be an ultimate product 
of the decomposition of vegetable and mineral matter under 
conditions producing naphtha, petroleum, mineral tar, and 
asphaltum, or hard bitumen. ‘These substances merge into 
each other by insensible degrees, and it is impossible to dis- - 
tinguish any well-defined dividing line between mineral tar 
and asphaltum. 

Deposits of asphaltum are quite common, especially in 
tropical regions. The chemical composition of the different 
deposits differs considerably, but all have the luster and 
general appearance of pitch. As usually found, asphaltum 
has the appearance of coal; it varies in consistency from a 
bright pitchy condition to that of thick viscid mineral tar. 

The composition of pure asphaltum or bitumen is about as 
follows: 


Garboms. Seige csi an aueie be ction eee 85 
Hydrogen. enter eee 12 
OXY COIN ans afer eines renee eee 3 

Total poche ee ee eee ee 100 


The color of asphaltum is a deep black, with a slight 
reddish tinge; it possesses a peculiar aromatic odor which, 
though scarcely perceptible at ordinary temperatures, is 
very strong at a boiling temperature. At ordinary temper- 
atures, its specific gravity is about 1.03. The consistency of 
pure asphaltum at different temperatures is as follows: 


Degrees Fahr. Consistency. 
Under d0s 4a, mona Solid and brittle. 
50, 00.0 Osean rene Soft and plastic. 
VOptGes- 00 a oe ae aaa Pasty. 

90 (6 120 ee eee Glutinous. 

A DOVE 20S ce an aree Liquid. 


Pure asphaltum is too brittle at low temperatures, and toe 
soft at high temperatures, and does not offer sufficient 


PAVING: 1137 


resistance to wear, to be satisfactory for paving purposes 
without the admixture of some other material. Conse- 
quently, an artificial mixture of bitumen, pulverized lime- 
stone, and sandstone is used. 


1837. Coal Tar.—The tar or pitch resulting from the 
distillation of bituminous coal in the manufacture of coal 
gas resembles natural bitumen so closely in external appear- 
ance that it was at one time thought to be equally valuable 
for paving purposes; it is often called paving pitch. 
Attempts to “use it for pavements instead of asphaltum, 
however, have generally resulted in failure. Its use for 
paving purposes is now confined to filling the joints between 
paving blocks, for which purpose it has been found valuable. 


1838. Clay; Paving Brick.—Bricks are composed 
of clay hardened by the process of burning. Pure clay isa 
soft, opaque material, white in color, and somewhat oily to 
the touch; it has a characteristic odor when breathed upon. 
It is infusible and insoluble, though it absorbs water rapidly. 
When burned at a sufficiently high temperature, however, 
it becomes very hard and almost non-absorbent. 

Natural clay consists of a hydrated silicate of alumina, 
usually in combination with more or less iron, lime, magnesia, 
alkalies, and other substances. The character of clay and 
its fitness for any purpose depend largely upon its ingredi- 
ents. For bricks, it should be rich in silica in a combined 
state, but should not contain silica in the form of sand, as 
the sand, having no combining properties, impairs the 
strength of the brick. The presence of lime in clay used 
for the manufacture of paving brick is to be carefully 
avoided; when exposed to the water it absorbs moisture and 
causes disintegration. Iron, though it renders clay fusible, 
is rather advantageous in paving bricks, as it makes them 
more homogeneous. Magnesia does not greatly affect the 
character of clay, though under certain conditions it may 
cause the bricks to crack. From 1 to 3 per cent. of alkali 
renders clay fusible; in small quantities, however, alkalies 
are found in the best of clays.) 


1138 PAVING. 


The color of clay is of little if any importance as relating 
to the quality of bricks; it is due chiefly to the presence of 
metallic oxides, but may be due to the presence of organic 
substances. Bricks manufactured from clay containing iron 
may be red, yellow, or blue, according to the quantity of the 
oxide present and the degree of heat to which they have been 
subjected in burning. A white color indicates the absence 
of metallic oxides or other color-producing ingredients. 

Common bricks are not suitable for paving purposes, even 
when hard burned. Though they will sustain a light traffic 
for a number of years, they will not endure a heavy traffic, 
and will, intime, disintegrate from the action of moisture 
and frost. Bricks made of suitable clay, however, are very 
strong and durable, and will endure the severest frost 
without injury. 

Bricks suitable for paving should not contain more than 
one per cent. of lime and should be burned specially for the 
purpose. When tested upon their flat. sides, they should 
offer a resistance to crushing of not less than 8,000 pounds 
-per square inch, should not absorb more than 5 per cent. of 
their weight of water, and should be so tough that when 
struck a quick blow on the edge witha 4-pound hammer, the 
edge will not spall or chip. They should be of uniform size, 
straight, square on edges, and free from fire-cracks or 
checks. When broken, the fracture should appear smooth 
and the texture uniform, and when struck together, they 
should have a firm, metallic ring. 


1839. Wood.—Many different kinds of wood have 
been employed for paving. In general, it may be stated that 
the hard woods have not been found to be the most suitable for 
pavements; the close-grained, pitchy, soft woods wear better 
and afford better foothold for horses. In the United States, 
cedar and cypress are the varieties that have been most 
extensively used, though juniper, tamarack, and yellow pine 
have been used to some extent. Of recent years, mesquite, 
a very hard wood that grows in abundance in Texas and 
Mexico, has been used with quite satisfactory results; two 


PAVING. 1139 


varieties of Australian hard wood have also been tried. In 
Europe, most varieties of the pine species and also oak, 
deal, ash, and elm have been tried for paving; Memel and 
Dantzic fir appear to be generally preferred. Whatever 
variety of wood is used, it should be of uniform quality, 
close-grained, perfectly sound, and free from knots, sap, and 
all indications of incipient decay. 


1840. Sand.—This is an aggregation of small frag- 
ments or angular grains of silicious, argillaceous, calcareous, 
or other material, resulting from the disintegration of rocks 
and mineral matter. It is crystalline in structure and gen- 
erally of a silicious nature. Sand is used as a foundation for 
wood, brick, and broken-stone pavements, as a cushion, or 
bed, for stone and brick pavements, and as joint-filling for 
all kinds of block pavements. It is a suitable material for 
such purposes; when confined, it is quite incompressible, 
yet readily adjusts itself to the form of the compressing 
surface. 

The sand used for paving purposes should be clean and 
sharp and preferably silicious. It should be free from loam 
and clay. The cleanness of sand may be tested by rubbing 
it in the palm of the hand and noticing the amount of dust 
remaining after throwing the sand away. When damp, the 
cleanness of sand may be tested by pressing it between the 
fingers; if it is clean it will not stick together, but will fall 
apart upon removing the pressure. The sand should be 
sharp, that is, the grains should be angular in form and not 
rounded. The sharpness of sand may be quite accurately 
judged by rubbing it between the fingers and noticing the 
feeling, or by crushing it near the ear and noticing the 
harshness of the sound. In erdinary sand the voids will 
occupy from about .3 to.5 of the total volume; the more the 
variation in the sizes of the grains and the more angular the 
grains, the less will be the proportion of voids. 





1841. Concrete.—This is an artificial stone composed 
of fragments of hard material of a rocky nature, cemented 
together by mortar or other cementing material. The 


1140 PAVING. 


aggregation of rocky fragments is called the aggregate, 
and the cementing material is called the matrix. The 
aggregate may consist of broken stone, gravel, shells, frag- 
meénts-ot brick, furnace Slag, cinders, etc.sl nemin ire 
should preferably consist of hydraulic-cement mortar, but 
may consist of lime mortar, or other cementing material. 

The condition essential to a strong and satisfactory con- 
crete appears to be that the fragments of material composing 
the aggregate be of small dimensions, and that the proportion 
of mortar be not greater than is sufficient to fill the voids 
entirely. As the material composing the matrix is generally 
more expensive than that composing the aggregate, the 
greatest economy is effected by using fragments of different 
sizes for the aggregate, thus reducing the proportion of 
voids to be filled by matrix. Concrete for the foundations 
of pavements should be composed of materials of good 
quality, dense, and homogeneous. The voids of the aggre- 
gate should be thoroughly filled with the mortar of the 
matrix, and the proportions of the latter should be such that 
the voids in the sand will be completely filled by the cement 
paste. The entire mass should be thoroughly mixed before 
water is added, and only sufficient water should be added to 
give it the proper consistency; the water should be added 
in small quantities, the concrete being briskly and thoroughly 
mixed. In Pabléssand Formulasasseiven,actables orm ia. 
gredients for Hydraulic-Cement Concrete. 

The concrete should be deposited in layers not exceeding 
6 inches in thickness, and thoroughly but hghtly tamped 
until a thin film of moisture appears on the surface. When 
there are two layers, the surface of the first layer should be 
moistened before spreading on the second. 


1842. Bituminous Cement.—This cement may be 
composed of coal-tar pitch, gas-tar, and creosote oil. The 
following proportions are commonly used: 


Coal-tatpitc hte tren eee 100 pounds. 
(aS, tartan ate ee eee 4 gallons. 
(LEOSOCEROI scree scp ncn tae 1 gallon. 


PAVING. | 1141 


These proportions are varied to some extent, according to 
the quality of the various ingredients employed. The mix- 
ture is prepared by being melted and boiled from one to 
two hours, and used while at a boiling heat. This cement 
is used principally for filling the joints of stone-block pave- 
ments, but it is also used for making bituminous concrete 
for pavement foundations. 

A paving cement that is also much used for joint filling is 
composed of creosote oil and the residuum obtained from the 
direct distillation of coal tar. The proportions commonly 
used are 1 gallon of oil toabout 45 pounds of residuum,though 
they vary considerably. The ingredients are melted to- 
gether in suitable iron boilers, and used ina boiling state. 
Asphalt is sometimes used and also coal tar, as well as a 
mixture of asphalt and coal tar. The names bituminous 
cement and asphaltic cement are applied quite gener- 
ally and indiscriminately to such mixtures, however, 
regardless of whether they contain asphalt or not. 


THE CONSTRUCTION OF PAVEMENTS. 


STONE PAVEMENTS. 

1843. Cobblestone Pavement.—This pavement 
consists of cobblestones of nearly uniform size bedded in 
sand. The roadway is excavated to the required depth and 
form, and upon this foundation is spread a layer of clean 
sand or fine gravel not less than 10 inches in thickness. In 
this bed of sand or gravel are set small round boulders or 
field stone; they are set upon their small ends, with their 
greatest dimensions vertical. The stones are generally 
from 4 to 8 inches in horizontal dimensions, the small stones 
being placed in the center and the large ones on the sides 
of the roadway. After the stones are set, they are rammed 
with a heavy ram until they are settled to a firm and solid 
bearing in the bed. After the pavement is thoroughly 
rammed, a layer of sand or fine gravel about two inches in 
thickness is spread over it, A portion of the cross-section 


1142 PAVING. 


and plan of a cobblestone pavement is shown in perspective 
in Fig. 431; pis the pavement of cobblestone, s is the bed 






eee 
eB eae ae 













= eos < aro 
AS pow ole = cacy 
EEE EE EA EERE 
oe £ MOS Op CS mee ; ax 
on 2 Ol SOx Res 


FIG, 431. 


of sand or gravel, ¢ is the natural earth foundation, and £ is 
the curb. 


1844. Belgian-Block Pavement.—This form of 
pavement superseded the cobblestone, and, as a natural 
result, its construction is similar. It was first used in Bel- 
gium, whence its name. <A sand foundation is prepared 
much the same as for cobblestone, though it is generally 
only about six inches in depth. The stones are cubical 
blocks of trap or similar rock, generally from 5 to 7 inches 


































































































Fic. 482. 


in horizontal dimensions, and from 6 to 7 inches in depth. 
They are laid in parallel courses perpendicular to the axis of 
the street. After ramming, the surface of the pavement is 


PAVING. 1143 


covered with clean sand, which is swept into the joints. A 
portion of the plan and cross-section of a Belgian-block 
pavement is shown in perspective in Fig. 432; 0 is the pave- 
ment of Belgian block, s is the bed of sand or gravel, @ is 
the natural earth foundation, and £ is the curb. 


1845. Granite-Block Pavement.—Neither cobble- 
stone nor Belgian-block pavements are constructed now on 
any extensive scale, both having been superseded by the 
rectangular granite-block pavement, which has proved to be 
the most enduring and economical pavement for roadways 
subjected to constant and heavy traffic. 


1846. The foundation for granite-block pavement 
should be firm and unyielding, hydraulic-cement concrete 
being the best material for this purpose. The concrete 
foundation, or base, should be from 4 to 9 inches in thick- 
ness, according to the nature of the traffic; a thickness of 
6 inches will sustain a very heavy traffic. The foundation 
should be well laid and thoroughly tamped, and should be 
allowed sufficient time to thoroughly set and dry before the 
paving blocks are laid. ‘The surface of the concrete foun- 
dation should be parallel to the surface of the finished 
roadway. 


1847. Cushion Coat.—A cushion coat of suitable 
material should be spread upon the foundation to receive 
the paving blocks. The material for the cushion coat 
should be incompressible and of such a nature as to adjust 
itself easily to the irregularities of the paving blocks. For 
this purpose, fine, clean, dry sand is an excellent material; 
it must be perfectly free from pebbles and perfectly dry. It 
is a well-established principle that moisture must not be 
present in the foundation, as frost will have a destructive 
effect upon it. The layer of sand should be from about 
three-quarters to one inch in thickness. <A better cushion 
coat is afforded by a layer of asphaltic cement one-half inch 
in thickness; this is probably the best possible cushion coat 
for granite-block pavements, 


1144 PAVING. 


1848. Size and Form of Blocks.-—The paving 
blocks should be rectangular in form, of uniform depth, and 
nearly uniform width. A depth of 7 inches is generally 
considered suitable. Their width should be from 3 to 
34 inches, or, say, such that four blocks placed side by side 
will make a total width of 14 inches. The lengths of the. 
blocks should vary from about 9 to 12 inches. The blocks 
should be perfectly rectangular; wedge-shaped blocks should 
not be allowed in the pavement; should any slightly wedge- 
shaped blocks be permitted, however, they should be set 
with the widest edge downwards. 


1849. Laying the Blocks.—The blocks should be 
laid in parallel courses; those of the roadway should be laid 
with their greatest dimensions perpendicular to the axis of 
the street, while at each outer edge about three rows of 
blocks should be set parallel to the curb to form the gutter. 
The blocks of each course should all be of the same width, and 
their lengths should be so arranged as to break joints with 
the adjacent courses. The blocks should be laid singly, 
stone to stone, with the least possible width of joints, the 
courses being commenced at the gutters and laid towards 
the middle. 


1850. Ramming.—After being set, the blocks should 
be thoroughly settled into the sand cushion by being 
rammed with a ram weighing not less than fifty pounds and 
having a bottom diameter of not less than three inches. 
Stones that sink below the general level should be taken up 
and the sand bedding increased sufficiently to bring them to 
the required height. 

The process of ramming should never approach nearer 
than about twenty-five feet to the edge of the pavement 
that is being laid. 


1851. Joint Filling.—The joint filling should be an 
impervious material. Sand and gravel do not make an 
impervious filling, and, consequently, are not suitable for 
the purpose., A grout Pemeeea of lime or cement mortar 
is not sufficiently elastic, and will become loosened and dis- 


PAVING. 1145 


integrated by the vibrations produced by the traffic. The 
best joint filling is a bituminous concrete composcd of 
bituminous cement (Art. 1842) and gravel. In applying 
this filling, the joints should be first filled with gravel to 
a depth of about two inches; then the hot pitch should be 
poured in, filling the joints to the depth of about one inch 
above the gravel; then the gravel and pitch should be added 
alternately until the joints are filled to within half an inch 
of the top; the remainder should then be completely filled 
with pitch, over which fine gravel should be sprinkled. The 
joint thus formed is impervious to moisture; it adds con- 
siderably to the strength of the pavement and makes it less 
noisy. : 

In Fig. 433 is shown a partial perspective view of a road- 
way paved with granite blocks on aconcrete foundation; ¢ is 






















































































































































































ot 
yO"s 
Me”, 





" 
ME ie 
ro Cy 
AERA 


x 


——— 
(od (iy, 
ae), 


WoO ade 


PAagarg 





Fic. 433. 


the natural earth foundation, c is the concrete base, s is the 
cushion coat, and ¢ is the course of granite blocks. The 
curb & should generally be about 5 inches wide and 18 inches 
deep; / is the sidewalk flagging. 


1852. Sandstone Block Pavements.—These pave- 
ments are of two general classes. The best pavements of 
sandstone blocks are very similar to the granite-block 
pavements. The blocks are somewhat wider, being gen- 
erally about four inches in width, and the cushion of sand is 
deeper, being sometimes three inches in depth. The con- 
crete foundation and bituminous joint filling are substantially 
the same. 

In second-class sandstone block pavements, the blocks are 


T. IV ,—2e2 


1146 PAVING. 


more or less irregular in form, and the concrete foundation 
is omitted. The blocks are laid on a foundation of sand 
varying from 10 to 18 inches in depth, according to the 
character of the subsoil; the joints are filled with sand. 


1853. Broken-Stone Pavement; Macadam.— 
Macadam’s system of broken-stone pavement is generally 
found quite satisfactory for roadways in suburban districts. 
The construction of broken-stone roads was considered in ~ 
Arts. 1689 and 1690, and but little will be added to 
what is there said. 

The following important conditions are essential to the 
construction of a satisfactory broken-stone pavement: 


1. The thorough drainage of the subsoil, artificial 
drains being constructed when necessary. 


2. The removal of all vegetable and perishable matter 
from the roadbed foundation. 


é..-The ‘excavation of the) natural soilstossochmccnrn 
as may be required by the thickness of the proposed cover- 
ing; if necessary to excavate deeper than this in order to 
remove such material as is liable to decay, the deficit should 
be filled with gravel, sand, hardpan, or the best similar 
material obtainable in the locality. 


4. The thorough compacting, by rolling, of the road- 
bed thus formed, before the application of the covering 
material. 


5. The spreading of a layer of gravel upon the roadbed 
before placing the broken stone, when the natural founda- 
tion is of the nature of clay. 


6.- The use of the best material’ for the brokensstone 
that is obtainable in the locality, and, in general, the use 
of fragments of different sizes and different degrees of 
hardness. 


?7. The exclusion of all clay and loam from the broken- 
stone covering material, and the use of a sufficient quantity 
of clean sand, gravel, or stone dust, and small fragments to 
completely fill the voids. 


PAVING. 1147 


8. The compacting of the broken-stone covering, by 
rolling witha heavy roller, until it is thoroughly consolidated 
and its surface is impervious to water. 


WOOD PAVEMENTS. 


1854. Different Systems.—Many different methods 
of constructing wood pavements have been tried, and a 
number of systems have been patented. The different 
systems vary with.regard to the form of blocks, of which a 
great variety of forms have been used. In several systems 
the blocks are treated with chemicals. By far the greater 
number of these systems have proved unsatisfactory, and at 
the present time it is quite generally accepted that the best 
~as well as the simplest form of wood pavement consists of 
rectangular or cylindrical blocks set on a solid foundation 
with the fiber vertical and the joints filled with an impervious 
cement. 


1855. Foundation.—A solid, unyielding foundation 
is as essential to a satisfactory wood pavement as to any 
other kind; in the United States, however, they have very 
commonly been constructed with insufficient and unsuitable 
foundations. In most cases, the blocks have’ been set 
either in a layer of sand spread upon the natural earth 
foundation or upon plank laid upon the sand. Such foun- 
dations do not sufficiently protect the subsoil, but allow the 
water to penetrate until the soil becomes saturated and 
yielding. In this condition it can not furnish a firm and 
solid support to the paving blocks, but will allow them to 
settle unevenly under the traffic, causing the surface of the 
pavement to become very rough and uneven. This is 
the most common defect of wood pavements, and in nearly 
all cases is the cause of the rough surface for which wood 
pavements are so generally condemned. 

A solid, unyielding, and impervious foundation, that will 
not only distribute the weight of the concentrated loads 
over a sufficient area of the natural foundation, but will 
also protect the foundation from becoming saturated and 


1148 PAVING, 


unstable, is absolutely essential to the stability and per- 
manence of any pavement. Hydraulic-cement concrete 
forms the best foundation for this purpose. The construc- | 
tion of the foundation is essentially the same as for granite- 
block pavements (Arts. 1841 and 1846). As _ wood 
pavements are not adapted to as heavy traffic as granite- 
block pavements, however, the foundations for the former 
need not generally be of as great depth; a layer of concrete 
4 inches in thickness will in many cases be sufficient for the 
foundation of wood pavements. 

A foundation similar to that used for telford pavements 
has been employed for wooden-biock pavements with quite 
satisfactory results, in cases where the subsoil is of a clayey 
nature, with occasional soft places. This foundation con- 
- sists of two Jayers of stone and gravel; the first layer is 6 
inches in thickness, composed of large stones laid with their 
largest face upon the natural foundation, and thoroughly 
wedged together with all chinks filled with smaller stones, 
after the manner of the telford foundation; the entire sur- 
face is then covered with a layer of wet gravel and thor- 
oughly compacted by rolling. Upon this is placed a layer 
of broken stone 2 inches in thickness, which is also covered 
with wet gravel and thoroughly compacted by rolling. A 
thin layer of stone is then spread over this, and the whole 
then covered with a course of 1-inch plank. 

Sand, gravel, and plank foundations are constructed in 
various ways. In some cases, the foundation consists of a 
layer of clean sand and gravel about 6 inches in depth, 
thoroughly compacted by rolling. In other cases a layer of 
clean sand about 3 inches deep is thoroughly compacted and 
covered with a course of 2-inch plank laid close together 
and lengthwise of the street, the ends and center of each 
plank being supported upon an 8" x 1” stringer firmly 
bedded in the sand. Sometimes the layer of sand and 
gravel is entirely omitted and the plank laid directly upon 
the natural foundation, which is finished to the proper 
form and in which are bedded stringers to support the 
planks. 


PAVING. 1149 


1856. Cushion Coat.—Where a concrete foundation is 
used, a cushion coat one-half inch in thickness, composed of 
either fine, clean, dry sand, or asphaltic cement, should be 
spread upon the foundation to receive the blocks. Whena 
cushion coat of sand is used, it should be perfectly dry, arti- 
ficial heat being employed to dry it if necessary. The 
cushion coat is sometimes omitted, however, and the biocks 
set directly upon the concrete foundation. Where the 
foundation is composed of sand and gravel only, the blocks 
are set directly upon the sand and gravel; they are also set 
directly upon the planks, when a plank covering is placed 
upon the sand and gravel foundation. 


-1857. Form and Size of Blocks.—Of the many 
different forms of paving blocks that have been tried, only 
two forms are now commonly used, namely, the rectangular 
‘and the cylindrical. The rectangular blocks are generally 
required to be 3 inches in width, 6 inches in depth, and 
about 9 inches in length. These are the dimensions usually 
preferred, the lengths being allowed to vary somewhat; 
lengths of from 6 to 12 inches are sometimes specified, but 
blocks longer than 9 inches have been found to be liable to 
split. The blocks should be perfectly rectangular. The 


cylindrical or “‘ 


round” blocks are generally required to be 
from 4 to 8 inches in diameter and 6 inches in depth (length), 
the diameter of 4 inches being preferred. Each block 
should be of uniform cross-section throughout its length, 
with its ends truly perpendicular to its axis. When placed 
in position in the pavement, the fibers of all blocks should 
be vertical. As paving blocks usually decay before they 
wear out, it is probable that blocks of less depth than 
6 inches could be employed to advantage. 


1858. Laying Rectangular Blocks.—Rectangular 
blocks should be set in parallel courses with their lengths 
perpendicular to the axis of the street or direction of the 
travel. The blocks in each course should break joints with 
the blocks of the adjacent course by a lap of not less than 
2 inches. Adjacent to each curb, about 3 courses of blocks 


1150 PAVING. 


should be laid parallel to the curb to form the gutter; it is 
a good plan to leave out the course adjoining the curb until 
expansion has ceased, filling the unpaved space with sand. 
At street intersections the courses should be laid diagon- 
ally. In Fig. 484 is shown a portion of a street pavement 














Fic. 434. 


of rectangular wooden blocks on concrete base; e is the 
natural earth foundation, c is the concrete base, w is the 
wearing surface of wooden blocks, 6 is the bituminous, or 
asphaltic-cement cushion coat and joint filling, and ¢ is the 
joint filling of hydraulic-cement grout. 

The joints should in no case exceed 2 of an inch, and pref- 
erably should not exceed + of an een in iain Wide 
joints permit the fibers of the wood to spread, thus render- 
ing it more absorptive and hastening its destruction and 
decay. The tendency of the present practice is towards 
narrower joints; in some of the wood pavements constructed 
in recent years, the blocks have been laid with close joints. 


1859. Laying Cylindrical Blocks.—Cylindrical, or 
round, blocks should be set in close contact with each other, 




















Fic. 435. 


extending across the street in parallel rows. Split blocks 


PAVING. 1151 


should be set along the curbs and wherever it is necessary 
for the edge of the pavement to join upon a straight line. 
No split blocks should be laid in the main portion of the 
pavement, however. 

In Fig. 435 is shown in perspective a portion of a wooden- 
block pavement composed of cylindrical blocks on a sand 
and plank foundation; ¢ is the natural earth, s is the sand 
foundation, / is the plank covering, and w the wearing sur- 
face of wooden blocks, # is the curb, and / is the flagstone 
of the sidewalk. 


1860. Ramming.—After the blocks have been laid, 
they should be rammed with a hand rammer, but the 
amount of ramming required will depend to some éxtent 
upon the kind of foundation employed. Where the blocks 
rest upon a sand and gravel foundation, or upon a cushion 
coat of sand spread over a concrete foundation, the blocks 
should be rammed with a rammer weighing not less than 
50 pounds, until settled to a solid bearing. All blocks that 
sink below the general level of the pavement should be taken 
up and sufficient sand added to raise them to the required 
height. Where the blocks rest directly upon the concrete 
foundation, or upon the plank covering of the sand or gravel 
foundation, very little ramming is required. 


1861. Filling the Joints.—Different materials and 
various methods are employed for filling the joints of wood 
pavements, and with varying results. It is essential that 
the joints be filled with a material impervious to water; a 
filling of sand or gravel is not impervious, and can not give 
the best results. 

Joints of rectangular block pavements are sometimes 
filled with a grout composed of one part Portland cement 
and two parts fine, clean, sharp sand. Thisis a good filling 
material, but the best results, however, are obtained by fill- 
ing the lower two or three inches with bituminous cement 
and the remainder with the hydraulic-cement grout. The 
grout forms a good wearing surface and _ protects the 
bitumen from being softened by the direct heat of the sun. 


1152 PAVING. 


In cylindrical block pavements, the spaces between the 
blocks are of considerable size and it is advantageous to add 
gravel to the bituminous cement filling. The spaces should 
first be filled to a depth of about 2 inches with clean, well- 
screened gravel, in which the sizes of the pebbles vary from 
about + to 4 inch indiameter. Sufficient hot paving cement 
should then be poured in to fill the joints to a depth of 
about 2 inches above the gravel, then sufficient gravel added 
to fill them even with the top of the pavement, then the hot 
paving cement again poured into the joints until they are 
completely filled and will absorb no more. After the joints 
are thus filled, a layer of clean, dry sand should be spread 
uniformly over the surface of the pavement to a depth of 
about half an inch. 


1862. Expansion of Paving Blocks.—The expan- 
sion of wood in a direction perpendicular to its fiber, when 
exposed to moisture, is very considerable. The rate and 
amount of expansion, of course, varies for different woods 
and different conditions of seasoning, but the average 
expansion of ordinary pavements composed of untreated 
blocks will be about one one-hundredth, or say 1 inch in 
8 feet; the wood will usually attain its full amount of ex- 
pansion in from 12 to 18 months. If no provision is made 
for the expansion, it is liable to either displace the curbs or 
distort the pavement itself. In order to avoid this, the 
joints near the curbs may be left open, or the course adja- 
cent to each curb may be temporarily omitted and the 
spaces filled with sand; after the expansion has ceased, the 
pavement should be properly finished by filling the joints 
left open or setting the* courses "omitted. adjacentstoscne 
curbs. Paving blocks impregnated with oil of creosote, 
however, do not expand or contract to any appreciable ex- 
tent, and a pavement composed of such blocks may be 
finished complete at once. 


1863. Chemical Treatment of Paving Blocks.— 
The chief cause of the deterioration of well-constructed 
wood pavements that are sustained by suitable foundations 


PAVING 1153 


is the decay due to the action:of air and moisture. The 
wood, being porous, readily absorbs moisture, and the re- 
peated wetting and drying induce decay. For the purpose 
of preventing or retarding the decay, many different proc- 
esses of treating the wood with chemicals have been tried. 
It will be well to notice that the practice of dipping the 
blocks in coal tar or creosote oil is injurious rather than 
advantageous, especially in the case of green wood; it con- 
fines the moisture and green sap within the blocks, causing 
fermentation and rapidly destroying the strength of the 
fibers. Among the best and most effective of the chemical 
processes employed are the following: 


1. Burnettizing is the name given to a process that 
consists in impregnating the timber with a solution of chlor- 
ide of zinc, in about the proportion of 1 pound of zinc to 
4 gallons of water. This process also renders the wood 
incombustible. 


2. Kyanizing is the name of a process in which the 
timber is immersed in a saturated solution of corrosive sub- 
limate (bichloride of mercury) until the pores are filled with 
the solution. The proportions used are 1 pound of the 
corrosive sublimate to from 10 to 15 gallons of water, accord- 
ing to the strength required. 


3. Creosoting consists in impregnating the timber with 
the oil of tar or creosote, from which the ammonia has been 
removed. From 8 to 12 pounds of the oil is used per cubic 
foot of the timber treated, according as the timber is hard 
or soft. The timber is first thoroughly dried and then im- 
mersed in hot oil, or the latter is forced by pressure into 
the pores of the timber. 

Of these processes the last is the most effective, both from 
an economic and from a sanitary point of view, though each 
of the above processes, when properly applied, will prevent 
decay and thus lengthen the natural life of the wood. They 
greatly diminish the expansion and contraction and also 
render the wood practically impermeable, thus removing 
the objection to wood pavements from a sanitary point of 


1154 PAVING. 


view. The chemical treatments of paving blocks have very 
little, if any, effect upon the wearing properties of the wood, 
however, and the advantages gained appear to be so small 
as to render them of somewhat doubtful economic value. 
Where sound, well-seasoned paving blocks are obtainable, 
and the traffic is of such nature as to cause them to wear 
rapidly, little advantage will be derived from chemical treat- 
ment. At the present time the best European practice 
favors the use of untreated blocks. 


ASPHALTUM AND COAL-TAR PAVEMENTS. 


SHEET ASPHALT; ARTIFICIAL MIXTURE. 


1864. General Considerations.—The asphalt pave- 
ments of Europe and those of America differ somewhat in 
their construction, owing to the difference in the character 
of the materials used. The former are composed of lime- 
stone naturally impregnated with bitumen, while the latter 
are formed from artificial mixtures of bitumen, sand, and 
pulverized limestone. The pavements composed of the 
bituminous limestone become hard, smooth, and slippery 
under traffic, and are not so satisfactory in frosty latitudes 
as those constructed from the artificial mixtures; the sand 
contained in the latter material lessens its slipperiness. 
The methods of construction noticed here will be those em- 
ployed in the construction of asphalt pavements in the 
United States. 


1865. Sources of Supply.—For the first asphalt pave- 
ments constructed in the United States, the bituminous 
material was imported from Europe. The great cost of the 
material thus obtained led to the trial of other materials 
and directed attention to the large deposits of natural 
bitumen on the island of Trinidad, which could be imported 
into the United States quite cheaply. Very satisfactory 
results have been obtained with this material, which is 
known as Trinidad asphalt. An artificial mixture of re- 


PAVING. 1155 


fined Trinidad asphalt with sand and pulverized limestone 
has been found suitable for paving purposes under the 
climatic conditions prevailing in this country, and is now 
quite extensively used, especially in the Eastern States. 
The principal source of supply is a so-called ‘‘lake”’ of over 
100 acres in extent, and from 20 to 80 feet in depth; the 
supply from this source appears to be inexhaustible, for, 
when excavated, the material soon fills in again from the 
bottom and entirely obliterates the excavation. Asphalt 
from this source is known to the trade by the terms lake 
and live asphalt. There are also other and apparently 
older deposits that are much harder and dryer. Material 
from these deposits is known as overflow, land, or dead 
asphalt. 

A very pure asphalt that has recently come into use for 
paving purposes is obtained from a lake or deposit covering 
an area of several hundred acres in the State of Bermudez, 
Venezuela. This material is said to be a very superior 
quality of nearly pure bitumen, and pavements constructed 
with it are said not to rot from continual contact with water, 
as do the Trinidad and most otherasphalts. It is known as 
Bermudez asphalt. 

Many deposits of sandstone and limestone rock impreg- 
nated with bitumen are found in the United States. The 
deposits are found chiefly in California and Utah, although 
deposits of bituminous material are found also in Kentucky, 
Texas, Montana, Colorado, and Indian Territory. The use 
of this material for paving purposes has not been extensively 
developed, though it has been considerably used in Western 
cities, and with evidences of reasonably satisfactory results. 
Pavements constructed of this rock are less slippery than 
ordinary asphalt pavements, and also resist disintegration 
from moisture. 

Deposits of natural bitumen are also found in many locali- 
ties in the United States, chiefly in California; they are 
generally of a character similar to those of Trinidad and 
Venezuela. These deposits originate in so-called springs 
from which the mineral pitch exudes, having about the 


1156 PAVING 


consistency of thick molasses; this spreads over the surround- 
ing surface and in time becomes solidified. The deposits 
thus formed vary greatly in extent and consistency, but are 
generally quite pure. 

Considerable quantities of fine bitumen are also obtained 
from Cuba, Mexico, and Peru. 


1866. Foundation.—It is very essential that all pave- 
ments of an asphaltic nature be sustained by a solid, un- 
yielding foundation, as the asphalt is suitable for a wearing 
surface only. Two kinds of materials are employed for the 
foundation, namely, hydraulic-cement concrete and _ bitu- 
minous concrete. Each material has its advantages, but 
the hydraulic-cement concrete is generally preferred. The 
concrete foundations for asphalt pavements are usually from 
4 to 6 inches in depth, according to the character of the 
traffic and the nature of the subsoil. 


1867. Hydraulic Base.—Foundations of hydraulic- 
cement concrete are very solid and enduring when properly 
constructed, and are generally preferred. With this ma- 
terial, however, the bond between the foundation and the 
wearing surface is sometimes so imperfect as to allow the 
wearing surface to slip on the foundation and roll in waves 
under the traffic, or crack from extreme change of temper- 
ature. The bond is liable to be very imperfect when the 
wearing surface is laid before the concrete of the foundation 
has become set and thoroughly dry. A foundation com- 
posed of hydraulic-cement concrete is sometimes called a 
hydraulic base. It is constructed substantially as 
described for stone-block pavements (Arts. 1846 and 
1841). 


1868. Bituminous Base.—When bituminous con- 
crete is used for the foundation, it unites quite thoroughly 
with the wearing surface and-forms a strong bond. Al- 
though this renders repairs more difficult, it largely pre- 
vents the waving and cracking of the asphalt wearing 
surface. A foundation composed of bituminous concrete is 


BASVANiG. 1157 


known asa bituminous base. It is commonly constructed 
by spreading a layer of clean, well-screened broken stone 
upon the prepared roadbed to the proper depth, and thor- 
oughly consolidating it by rolling, as in the construction of 
broken-stone roads, then pouring upon it a coating of coal 
tar or bituminous cement. The proportions used should be 
about one gallon of cement to each square yard of founda- 
tion. Bituminous concrete is less expensive than hydraulic- 
cement concrete. 


1869. Binder Course.—In order to effect a more 
complete bond, an intermediate layer of bituminous con- 
crete is commonly placed between the concrete foundation 
and the asphalt wearing surface; this is known as the 
binder course. It is composed of clean broken stone of 
small size mixed with bituminous paving cement. The 
stones should vary in size from 4 inch in smallest. to 1 inch 
in greatest dimension, and should be thoroughly screened. 
The stones, heated to a temperature of from 230 to 300 de- 
grees Fahr., should be mixed with the paving cement in 
the proportion of from three-fourths of a gallon to one gal- 
lon of cement to one cubic foot of stone. While hot, this 
mixture should be spread upon the base course to such a 
depth as will consolidate to a thickness of about 14 inches, 
and immediately rammed and rolled, while in a plastic con- 
dition, until thoroughly compacted. The binder course is 
substantially the same for either a hydraulic or a bituminous 
base. 


1870. Refining the Asphaltum.—The natural 
crude asphaltum contains much water and a considerable 
amount of earthy and organic matter and volatile oils, 
which must be removed in order to obtain a satisfactory 
paving material. The crude asphaltum is refined by heating 
it to a temperature of from 300 to 400 degrees Fahr. By 
this means the water and volatile oils are driven off and the 
asphaltum brought to a liquid state. In this state much of 
the earthy matter settles to the bottom and the lighter 
organic matter rises to the top; the intermediate liquid 


1158 PAVING. 


asphaltum is then drawn off as a refined product and 
allowed to cool. , 

The refined asphaltum is darker than the crude material, 
has a dull fracture, and a homogeneous appearance. As it 
is very brittle at ordinary temperatures, however, and has 
but slight cementing value, it is still unsuitable for paving 
purposes. 


1871. Asphalt Paving Cement.—In order to give 
the refined asphaltum the tenacity necessary for a satisfac- 
tory paving material, it is mixed, while at a temperature of 
about 325 degrees Fahr., with the residuum from the distilla- 
tion of petroleum, in the proportion of from 15 to 20 pounds 
of the petroleum residuum to 100 pounds of the refined 
asphaltum. 

The petroleum residuum is a thick, heavy paraffin oil; it 
varies considerably in composition, according to the nature 
of the petroleum and method of distillation. It varies 
greatly in character, even when obtained from the same 
source, and it as; therefore, necessary. to etteat. cdc mer se 
according to the nature of the oil obtained, as nearly as can 
be determined by analysis and examination. It is said that 
the best oil flashes at about 350 or 400 degrees Fahr., does 
not flow above 60 or below 32 degrees, and does not contain 
coarsely crystallizing paraffins when solid. 

On account of the varying nature of this oil, the entire 
amount to be used in the pavement should be thoroughly 
mixed together in a large tank before being added to the 
asphaltum, in order that the resulting cement may be rea- 
sonably uniform. When the refined asphaltum has cooled 
to a temperature of about 325 degrees Fahr., the residuum 
oil should be added and the entire mass agitated with a 
blower for 10 or more hours. Paraffin, which is the base of 
the petroleum residuum, is a substance of a very different 
nature from asphaltum, and hasa different specific gravity; 
consequently, they do not mix readily, and in a liquid state 
have a tendency to separate when allowed to stand without 
stirring. Thorough and constant agitation of the hot mix- 


PAVING. 1159 


ture is required in order to obtain a uniform product; great 
care must be exercised during the entire process, and it re- 
quires considerable experience to obtain a product of proper 
consistency and satisfactory for paving purposes. The 
product obtained is called asphalt paving cement, or 
asphaltic paving cement. 


1872. Asphalt Paving Material.—When the as- 
phalt paving cement has been prepared as described in the 
preceding article, sand and pulverized limestone are added 
in proper proportions in order to afford a suitable material 
for the wearing surface of the pavement. For the propor- 
tions of the materials, two general formulas are used which 
give nearly the same results. They are given in Tables and 
Formulas: Ingredients of Asphalt Paving Material. 

In order to obtain a satisfactory and homogeneous wear- 
ing surface for the pavement, the proportions of the differ- 
ent materials must necessarily be varied, according to the 
character of the materials used and the traffic upon the 
street. The proportion of asphaltic cement, and of the car- 
bonate of lime also, will depend upon the quality of sand. 
When suitable sand can be obtained, the proportion of 
carbonate of lime may be reduced or even omitted en- 
tirely. In any case the sand must be clean and free from 
clay. 

The asphaltic cement and sand should be heated separately 
to atemperature of about 400 degrees Fahr. The proper 
amount of pulverized carbonate of lime, while cool, should 
be mixed with the hot sand. This compound should then be 
mixed with the asphaltic cement at the required temperature 
and in the proper proportions. In order that the mixing may 
be perfect, the materials should be mixed in a special 
apparatus suited to the purpose. This asphalt paving 
material is laid upon the foundation or binder course, some- 
times in one and sometimes in two coats. When two coats 
are laid, the first coat should contain from 2 to 4 per cent. 
more asphaltic cement than given in the formulas 
referred to above. 


1160 PAVING. 


1873. Laying the Asphalt; Two Coats.—The first 
coat is called the cushion coat, and the second is called 
the surface coat. The cushion coat should be laid directly 
upon the binder course, or upon the concrete foundation 
when no binder course is used; it should be of such depth as 
will give a thickness of $ inch when consolidated by rolling. 
The surface coat is laid upon the cushion coat; the material 
for this coat should be delivered on the pavement in carts at 
atemperature of about 250 degrees Fahr. ; when the tempera- 
ture of the air is below 50 degrees, each -cart)should) be 
equipped with a suitable heating apparatus that will pre- 
vent the paving material from cooling below the proper 
temperature. 

The material of the surface coat should be carefully spread 
upon the cushion coat to such depth as to give a uniform 
surface and a thickness of 2 inches after being consolidated; 
hot iron rakes should be used for spreading the material. It 
should first be moderately compressed by hand rollers; a 
small amount of hydraulic cement should then be spread 
lightly over it, after which it should be thoroughly compacted 
by continued rolling with a heavy steam roller for not less 
than 5 hours for each 1,000 square yards of surface. 


1874. Laying the Asphalt; One Coat.—When the 
pavement is given only one coat of asphaltic material, it is 
laid in much the same manner as just described for the sur- 
face coat. The material should be: deliveredsingcartceae: 
temperature not below 250 nor above 310 degrees Fahr.; 
while in the carts it should be protected by canvas covers 
when the temperature of the air is below 50 degrees Fahr. ; 
it should be spread upon the foundation to such a depth as 
to give a uniform surface and a thickness of 24 inches after 
being consolidated. It should first be moderately compressed 
by hand rollers and a small amount of hydraulic cement 
spread lightly over it, the same as described above for the 
surface coat; after which it should be thoroughly compacted 
by rolling with a steam roller, weighing not less than 5 tons, 
followed by a second roller weighing not less than 10 tons, 


PAVING. 1161 


and the rolling should be continued for not less than 10 hours 
for each 1,000 square yards of surface. 

Wearing surfaces properly constructed in the manner 
just described would be suitable for very heavy traffic, 
and should be very enduring. It should be noticed, how- 
ever, that thinner wearing surfaces are by no means uncom- 
mon. In the lighter construction, the wearing surface 1s 
sometimes made 2 inches thick when laid directly upon the 
concrete foundation and 14 inches thick when laid upon a 
binder course. <A total thickness of 7 inches is quite common 
for asphalt pavements, including the foundation. 

A portion of a roadway paved with sheet asphalt pave- 
ment is shown in perspective in Fig. 436; e is the earth 


7 


‘Wg YLT! 
YMG: 


ffs 
Witt: 
WH YD 
VAM 


SS 
SN 
»S 





Fic, 436. 


foundation, c is the concrete base, 0 is the binder course, and 
a is the asphalt wearing surface; the gutter is paved with the 
granite blocks ¢; # is the curbstone, / the flagstone of the 
sidewalk, and s the sand bed on which the latter rests. 


1875. Gutter Surfaces.—The asphalt paving ma- 
terial described in Art. 1872 is not wholly impervious 
to water, and when in continual contact with water tends to 
rot or disintegrate. With some kinds of asphalt the disin- 
tegration is much more rapid than with others, while with 
asphalt obtained from certain sources, the paving material is 
said not to be affected by water. 

As pure asphalt is quite impervious to water, the gutter 
surfaces are sometimes coated with it in order to render them 
impervious and protect the underlying material. It is cus- 
tomary thus tocoat a width of about 12 inches adjacent to 


T. IV.—23 


1162 PAVING. 


each curb. Theasphalt should be placed upon the surface 
in a hot state and smoothed with hot smoothing irons, in 
order to impregnate the surface of the underlying asphaltic 
material with an excess of asphalt. 

In some cases the gutters are formed of granite blocks, 
bricks, or other suitable material not of an asphaltic 
nature: 


1876. Pavement Adjoining Railway Tracks.— 
When a roadway that is to be paved with asphalt contains 
street-railway tracks, the asphalt pavement should be joined 
not directly to the track but to a row of granite paving 
blocks laid along each side of the track. The foundation for 
the blocks should extend to the same depth as the bottoms 
of the cross-ties, but in other respects should be the same as 
the foundation of the roadway pavement. If this founda- 


seepepemaasithass: 



























































































































































[AON ISAT a MPA. o 

Me eeehy laste |: 

: ay eons! 
are 

we 

































































FIG. 437. 


tion is composed of bituminous concrete, the blocks should 
be laid directly upon it and imbedded in it while the bitu- 
minous cement is yet in a hot and plastic condition. If the 
foundation is composed of hydraulic-cement concrete, it 
should be covered with clean, fine, dry sand to a depth of 
about 2 inches, and the blocks should be laid upon and 
imbedded in the sand. 


PAVING. 1163 


These paving blocks should be laid before the layer of 
asphalt is placed upon the roadway; they should be laid as 
alternate headers and stretchers, so that when the asphaltic 
wearing surface 1s laid there will be a strong, tooth-like bond 
between the granite blocks andtheasphalt. The tops of the 
blocks should be even with the surface of the tread of the rails; 
the blocks should be laid with close joints and should be care- 
fully fitted against the stringers or the web of the rails. The 
joints between the blocks should be filled with coal-tar paving 
cement and gravel, much as described’in Art. 1851 for 
granite-block pavements. 

The space between the rails is sometimes paved with brick. 
In Fig. 437 is shown the portion of an asphalt-paved street 
adjacent to a street-railway track; @ is the asphalt wearing 
surface, 0 is the binder course, ¢ is the concrete base, and ¢ 
is the earth foundation, g isthe granite-block paving adjoin- 
ing the rail 7 of the railway track, which rests upon the 
wooden cross-tie ¢, and @ is the brick pavement between the 
rails. 


NATURAL, OR ROCK, ASPHALT. 

1877. Of What It Consists.—This material, as com- 
monly used for paving purposes in Europe, consists of 
limestone naturally impregnated with bitumen in such pro- 
portion that it may be softened by heat, and again consoli- 
dated in the required form when cooled under pressure. 


The material is known as rock asphalt, or bituminous 
rock. 


Sandstone rock similarly impregnated with bitumen is 
found in many places in the United States. This material 
has been used to some extent for paving purposes. ‘The use 
of natural asphalt for pavements, however, has scarcely 
passed beyond an experimental stage in this country. It 
may be stated that the granular nature of the rock renders 
these pavements less slippery than those of ordinary asphalt, 
and that they resist disintegration by moisture. It is also 
claimed that they stand high temperatures and cold, damp 
atmospheres equally well. 


1164 PAVING. 


1878. Foundation.—The foundation for this pave- 
ment should consist of concrete, substantially the same as 
described in preceding articles for the artificially prepared 
asphalt wearing surfaces. A binder course is not employed, 
however, but the natural asphalt, properly prepared, is laid 
directly upon the concrete foundation, which should pref- 
erably be of hydraulic-cement concrete. 


1879. Preparing the Asphalt.—Natural, or rock, 
asphalt is used to form the wearing surface. In order to 
be suitable for this purpose, the natural rock should contain 
from about 8 to 13 per cent. of bitumen. If it contains 
more than 13 per cent., it is apt to become soft in warm 
weather, and if it contains less than 8 per cent., it will not 
consolidate thoroughly or have sufficient bond; a range not 
ereater than) from 9 to 12 sper. cent. 1s=preterabiewsa un 
bitumen should be evenly distributed through the rock, 
whick should be of nearly uniform texture. In order to 
obtain the proper per cent. of bitumen, it is sometimes 
necessary to mix together rock obtained from different 
localities. 

The rock is first crushed to fragments of about the size 
of eggs, then ground to a fine powder. This powder is 
heated to the proper temperature (about 300 degrees Fahr.) 
to soften it to the required consistency. 


1880. Laying the Asphalit.—The hot material is 
delivered upon the roadway, and by means of hot iron rakes 
spread over the concrete foundation to such a depth as will 
compress to the required thickness. The thickness of the 
wearing surface after compression should not be less than 2 
inches; a compressed thickness of 2 inches requires a depth 
of about 3 inches for the uncompressed material. Proper 
precautions should be taken to prevent too much cooling of 
the hot asphalt while being transported to the pavement. 
The asphalt should be laid in dry weather and upon a per- 
fectly clean foundation, from which all loose or foreign 
substances have been removed. 

The material, when spread upon the foundation, should 


PAVING. 1165 


be vigorously rammed with hot cast-iron rammers of from 
6 to 8 inches in diameter, a sufficient number being used to 
ram the material to a compact condition while still hot. 
Soon afterwards the surface should be rolled with a light 
roller heated by an internal furnace. A small quantity of 
hydraulic cement should be swept lightly over the surface 
during the process of rolling, which should be continued 
until the asphalt is cooled. The final compression of the 
pavement is usually left to be effected by the wheels of the 
traffic. 

The method of laying the natural asphalt as here de- 
scribed corresponds to the European rather than the Ameri- 
can practice, though it may be considered as fairly repre- 
sentative of the latter. 


ASPHALT BLOCK PAVEMENTS. 


1881. Asphalt Paving Blocks.—These commonly 
consist of a mixture of asphaltic cement and crushed lime- 
stone molded into a form suitable for the purpose. A con- 
siderable portion of the crushed limestone will be dust, and 
the largest fragments should not exceed } of an inch in 
greatest dimensions; the asphaltic cement should be pre- 
pared as described in Art. 1871. The proportions should 
be such that the product will contain about 10 per cent. of 
the asphaltic cement. 

The materials should be heated to a temperature of about 
300 degrees Fahr., and mixed while hot, in a suitable appa- 
ratus. The mixing should be so thorough as to distribute 
the ingredients evenly through the entire mass. The mix- 
ture is then subjected to heavy pressure in molds somewhat 
similar to those of a brick machine, after which the blocks 
thus formed are cooled suddenly by immersing in cold 
water. The blocks are commonly 4 inches wide, 5 inches 
deep, and 12 inches long, though a size 24 x 6 x 8 inches is 
also used. 

It has been found impracticable to use sand in the manu- 
facture of asphait blocks, on account of its destructive 


1166 PAVING. 


effect upon the molds. Limestone is, therefore, used, but 
the resulting blocks are not so durable under traffic as 
though sand could be used. The blocks wear rapidly and 
are, therefore, not suitable for streets sustaining heavy traf- 
fic; they have given great satisfaction, however, on resi- 
dence streets, where the‘traffic 1s light. For such streets 
they form a smooth, clean, healthful, and tolerably durable 
pavement. 


1882. Foundation.—Asphalt paving blocks are com- 
monly laid upon a gravel foundation. The roadbed should 
be prepared to the proper form and grade, and thoroughly 
compacted by rolling andramming. A layer of clean gravel, 
from which have been screened all pebbles larger than 14 
inches in greatest dimension, should then be spread upon 
the roadbed to such depth as will give a thickness of 5 inches 
when compacted. After this is thoroughly compacted by 
rolling and ramming, a layer of fine, clean sand 2 inches 
in thickness should be spread upon it, to serve as a bed 
for the blocks: the surface of the sand bed should be 
exactly parallel to the intended surface of the completed 
roadway. 


1883. Laying Asphalt Paving Blocks.—The 
blocks should be laid in parallel courses upon the sand bed, 
with close joints and with their greatest dimensions per- 
pendicular to the ‘axis: of “the street; the blocks anieaen 
course should break joints with the blocks in the adjacent 
courses by a lap of not less than 4inches. In laying the 
blocks, the pavers should stand or kneel upon the blocks 
already laid, so as not to destroy the finished surface of 
the sand bed. In order to tightly close the lateral joints, 
each course, when laid, should be driven against the pre- 
ceding course by means of a heavy wooden maul, while the 
longitudinal joints should be closed by means of a lever 
operated against the end of each course at the curb. As 
fast as laid, the pavement should be covered with fine sand 
that is perfectly clean and dry. The blocks should then be 
rammed by striking upon an iron plate about 20 inches long, 


PAVING — 1167 


8 inches wide, and 1 inch thick, with a rammer weighing 
about 50 pounds; the ramming should continue until the 
blocks are firmly and solidly bedded, and present a uniform 
surface. All blocks sinking below the general surface of the 
pavement should be taken up and the sand bed increased 
sufficiently to bring them to the requiredheight. When the 
pavement has been thoroughly rammed, an _ additional 
amount of fine, clean, dry sand should be spread over its 
surface and swept into the joints. 

In such a pavement, the blocks will eventually become 
cemented together by the heat of the sun and the pressure 
of the traffic, so as to be practically water-proof. The view 












































of a portion of a roadway paved with asphalt block pave- 
ment is shown in Fig. 438; @ is the asphalt pavement, s is 
the sand cushion, g is the gravel base, and ¢ is the earth 
foundation. 


COAL-TAR PAVEMENTS. 

1884. Coal Tar as a Paving Material.—On ac- 
count of its close resemblance to bitumen, in external 
appearance, coal tar was formerly thought to possess much 
the same merits as a paving material, and various mixtures 
containing it have been tried for the wearing surface of 
pavements. Asarule, however, such pavements have not 
been satisfactory; the material contains volatile oils, which, 
by their oxidation on exposure to the atmosphere, leave it 
dry, inelastic, and liable to disintegrate rapidly. Coal tar is 

. 


1168 PAVING. 


also greatly affected by changes of temperature. Such 
defects make it very unsatisfactory as a cementing material 
for the wearing surface of pavements, and the use of coal 
tar alone for this purpose has been quite generally aban- 
doned. It has been found, however, that reasonably satis- 
factory results may be obtained. with a paving cement 
consisting of a mixture of coal-tar distillate and bitumen. 
Pavements containing such material are known as coal- 
tar distillate pavements, or simply as distillate 
pavements. 


1885. Foundation.—The foundation, or base course, 
may consist of either hydraulic-cement concrete or bitumin- 
ous concrete, though the latter would appear to be the more 
suitable for this pavement. It should be constructed in the 
usual manner, the distillate paving cement (hereafter de- 
scribed) being used for the cementing material. It should 
have a thickness, when thoroughly compacted, of at least 4 
inches, and, in some cases, a considerably greater thickness 
would be advantageous. 


1886. Binder Course.—This should be composed of 
clean, well-screened broken stone, mixed with the distillate 
paving cement. The stones should not exceed 14 inches in 
greatest dimension; they should be heated to a temperature 
of from 230 to 250 degrees Fahr. The paving cement should 
then be added in about the proportion of 1 gallon of cement 
to 1 cubic foot of stone, and the entire mass thoroughly 
mixed by machinery. ‘This should be spread-upon the base 
to such depth as will give a thickness of 14 inches after 
compression, and immediately and thoroughly rammed and 
rolled while in a hot, plastic condition. 


1887. Distillate Paving Cement.—This should 
consist of from 70 to 75 parts of coal-tar distillate and from 
30 to 25 parts of refined asphalt. The refined asphalt should 
contain not less than 60 per cent. of pure bituminous matter, 
and the tar distillate should be free from an excess of sooty 
matter, naphthaline, and creosote oils. 


PAVING. 1169 


1888. Materials for Wearing Surface.—A table 
of Ingredients for Distillate Pavements is given in Tables 
and Formulas, from which the proper proportions of the 
various materials may be taken. 

The sand should be clean, sharp, uniform, of suitable size, 
and perfectly free from clay or loam. Not more than 20 
per cent. should be retained upon a sieve of 20 meshes to 
the inch, and not more than 56 per cent. pass througha sieve 
of 70 meshes to the inch. The broken stone and stone dust 
should consist of such residue from the stone crusher as will 
pass a sieve of not more than 6 meshes to the inch. 


1889. Laying the Distillate Wearing Surface.— 
The materials should be heated to about 260 degrees Fahr., 
and thoroughly mixed by suitable machinery. The paving 
cement should be heated in kettles; the sand, stone dust, 
hydraulic cement, and sulphur, after being partly mixed, 
while cool, should be heated and more completely mixed in 
a revolving heater. The hot mixture should be delivered 
~ upon the roadway, and, by means of heated iron rakes or 
other suitable appliances, be spread upon the binder course to 
such depth as will give a thickness of 14 inches after con- 
solidation. It should then be immediately and thoroughly 
compacted by ramming and rolling while in a hot and 
plastic state. The material should be spread in such man- 
ner that, in attaching the new material to the edge of that 
previously spread, the joints will be at an angle of about 45 
degrees with the line of the street. In cool weather the 
carts delivering the material should be provided with canvas 
covers, to protect the material from excessive cooling. 

The pavement thus constructed should have a total thick- 
ness of not less than 6 inches, and should be thoroughly 
rolled lengthwise and crosswise until compacted to a hard 
and solid mass. 


1890. Gutters.—For pavements whose wearing sur- 
faces are constructed of coal-tar distillate, it will generally 
be advantageous toconstruct the gutters of granite blocks or 
of bricks laid upon a hydraulic base. 


1170 PAVING. 


BRICK PAVEMENTS. 


1891. General Conditions.—Although brick was 
one of the first of the materials used for paving, it was not 
extensively used for this purpose until recent years. It is 
not equal to granite as a paving material for roadways sus- 
taining an exceedingly heavy traffic, but when constructed 
in a proper manner and of suitable materials, upon a solid 
foundation, it forms a smooth, durable pavement, well 
adapted to moderate traffic. 

No standard methods of construction have yet been 
established for brick pavements; the practice varies consid- 
erably and the requirements of specifications differ greatly. 
There has been no definite standard adopted for the quality 
of the bricks to be used, and the language of specifications 
with regard to. it) is smore or less. vague. Wy Dhe- methods 
described below probably represent the best American 
practice. 


1892. Foundation.—In order that a pavement may 
be serviceable and enduring, it must be supported upon a 
solid, unyielding foundation; this is as essential for brick 
as for any other kind of pavement. The foundation of 
brick pavements should in all cases consist of hydraulic- 
cement concrete, constructed substantially as described for 
granite-block pavements (Arts. 1841 and 1846). In 
localities where broken stone and gravel are difficult to 
obtain, the aggregate of the concrete may consist of 
fragments of broken bricks. 

In some cases the foundation is formed by a layer of 
bricks laid flat-wise upon a bed of gravel spread upon the 
prepared roadbed, their lengths extending parallel to the 
curbs. Fine sand is swept into the joints of the bricks, and 
the whole is then covered with a cushion coat of sand. 

Many other kinds of foundations have been employed for 
brick pavements, such as sand, gravel, sand and boards, 
broken stone, etc. The only foundation for brick pavements 
that is to be commended, however, is the foundation of 
hydraulic-cement concrete. 


PAVING. baby 





1893. Cushion Coat.—A layer of fine, clean, dry 
sand should be spread upon the concrete foundation, to a 
uniform depth of $ inch, as a cushion coat to receive the 
bricks. It is essential that the sand for the cushion coat 
should be perfectly free from moisture; if necessary, it 
should be dried by artificial heat. The cushion coat is 
sometimes made as deep as 2 inches. 


1894. Form and Size of Bricks.—The bricks 
should be perfectly rectangular inform, with square corners 
and straight edges. They should be of the ordinary com- 
mercial size, which is about 8 xX 4 x 24 inches; all bricks 
should be of exactly the same size. 


1895. Laying the Bricks.—The bricks should be set 
edgewise upon the cushion coat, with their sides and ends 
in close contact. They should extend in parallel courses 
across the street with their lengths perpendicular to the axis 
of the street, and should be so laid that the bricks of adjoin- 
ing courses will break joints by a lap of not less than three 
inches. At street intersections, the courses should extend 
diagonally, so as to be approximately at right angles to the 
traffic. 


1896. Ramming.—After the.bricks have been laid, 
every part of the pavement should be thoroughly rammed 
with hand rammers weighing not less than 50 pounds. The 
ramming, however, should not approach nearer than within 
about 25 feet of the edge of the new pavement that is being 
laid. All bricks that sink below the general level of the sur- 
face of the pavement should be taken up and have sufficient 
sand added to the cushion coat beneath them to bring them 
to the required height. 


1897. Filling the Joints.—When the bricks have 
been settled to a firm and solid bearing by ramming, all 
joints should be filled full with a grout composed of equal 
parts of hydraulic cement and fine, clean, sharp sand. The 
entire surface should then be covered with a layer of sand 
4 inch deep. 


1172 PAVING. 


CURBING AND FOOTWAYS. 


CURBING. 


1898. Where Set.—With whatever kind of pavement 
a street is paved, it is the almost invariable practice to set 
thin slabs of stone or other suitable material along the outer 
edges of the roadway, to form the gutter and to sustain the 
adjacent earth or footwalk; these are known as curb- 
stones, curbing, or curbs. The upper edges of the 
curbstones are set level with the footwalk pavements, so that 
water can flow over the curbstones into the gutters. 


1899... Materials for Curbing.—The materials most 
commonly employed for curbstones are natural stones, such 
as granite, sandstones, etc., dressed to suitable form, and 
artificial stone, composed of hydraulic-cement concrete ; 
fireclay, cast iron, and wood are sometimes used for curbing, 
however. Natural stone is the material generally used for 
curbing in localities where obtainable; in localities where 
natural stone is not obtainable, artificial stone is probably 
the best material for the purpose, though slabs of burnt fire- 
clay, of the nature of bricks, make excellent curbs and are 
extensively used with brick pavements. Granite is generally 
considered the best material for curbs, though sandstone and 
limestone are both used. Cast iron and wood are not really 
suitable for the purpose. 


1900. Form and Dimensions of Curbstones.— 
These vary considerably in different localities; they are 
largely matters of appearance and not subject to rigid 
requirements of construction. Curbstones vary from 4 to 
12 inches in width, from 8 to 24 inches in depth, and are 
usually from 3 to 6 feet in length, according to the require- 
ments of specifications, depth of gutter, etc. The depth of 
a curbstone should always be sufficient to prevent it from 
turning over or tipping towards the gutter; this condition 
will depend somewhat upon its width also. The lengthof a 
curbstone should not be less than 38 feet. 


PAVING. 1173 


The front face of the curbstone should be hammer-dressed 
to a depth somewhat greater than that exposed above the 
gutter; where the sidewalk joins the curbing, the back of 
the curbstones should be dressed to a sufficient depth to 
allow the sidewalk pavement to fit closely against it. The 
ends of the curbstones should be dressed throughout their 
exposed depth, and the portion below the gutter surface 
should be so trimmed off as to permit them to be laid with 
close joints. The top surface of the curbstones should be 
dressed to a bevel corresponding to the slope of the adjoin- 
ing sidewalk. ~The bed of the curb should generally be not 
less than 6 inches in width. Curbstones are sometimes 
made hollow, in order to provide conduits for electric wires, 
pipes, etc. 


1901. Setting the Curbing.—Great care should be 
exercised in setting the curbing; it should be set true to line 
and grade. The curb should always be bedded firmly upon 
a solid foundation; the work should be thoroughly and sub- 
stantially done, in order that the curbing will keep its 
proper position and not sink or tip towards the gutter. 

Curbing is set in various ways; it is sometimes set directly 
upon the earth foundation, scmetimes upon a gravel, and 





Fic. 489. 


sometimes upon a concrete foundation. The last is much 
the best method. The curb should be set in a concrete 


1174 PAVING. 


foundation, continuous with the foundation of the pave- 
ment. A curb thus set in concrete is shown in Fig. 439; 
e is the natural earth, c is the concrete foundation, 7P is 
is the wearing surface of the roadway pavement, £ is the 
curbstone, and. /f is the sidewalk flagging; the common 
dimensions of the different parts are marked in the figure. 
The wearing surfaces of roadway pavements are of differ- 
ent thicknesses, according to the material used. 


FOOTWAYS. 


1902. General Requirements.—A footwalk is sim- 
ply a road for pedestrians instead of for vehicles. ‘The dif- 
ference is one of degree rather than character, and the 
principles which govern the construction of roadway pave- 
ments should govern the construction of footway pavements 
also. Though the travel upon a footway is of a lighter 
character than that upon a roadway, and the construction of 
the footway is less massive and costly, it should not be less 
thorough, complete, and well suited to the end in view, nor 
less durable, than that of a roadway. 


1903. Materials for Footways.—The materials 
most commonly used for footways are natural and artificial 
stone, brick, asphalt, wood, tar, concrete, and gravel. 

Natural stone footways are generally durable and satis- 
factory; sandstone, limestone, and granite are employed. 
Of these a good quality of sandstone gives the most satis- 
factory results. When of compact texture, it absorbs com- 
paratively little water and soon dries after rain; it also 
wears well without becoming very slippery. Limestone 
does not generally wear well; granite, though it wears ex- 
ceedingly well, becomes very slippery. 

Artificial stone is extensively used as a paving material 
for footways. When properly constructed from good ma- 
terials, it forms one of the most satisfactory of footway 
pavements. These footways are constructed in two ways, 
namely, from slabs of the artificial stone manufactured at a 


PAVING. 1195 


factory and laid in the same manner as natural stone, and 
by forming the artificial stone in its proper position in the 
footway. The latter plan is the more commonly adopted. 

Bricks of suitable quality, if carefully laid on a proper 
foundation, form an excellent footway pavement for the 
streets of residence and suburban districts, and also for the 
main streets of small towns. 

Asphalt pavement forms an excellent footway; it is 
durable, agreeable to walk upon, and does not wear slip- 
pery. Itis used both in the form of sheet asphalt and in 
the form of compressed tiles. 

lVood in the form of planks has been extensively used for 
footwalks. Footways of this material are cheap in first cost, 
and when in good condition are pleasant to walk upon. 
They soon get in bad condition, however, and not only re- 
quire constant attention and repairs, but also become un- 
pleasant and even dangerous for pedestrians. 

lar concrete has been quite extensively used for foot- 
ways in several cities. They have not proved satisfactory. 
They soon become so worn and in such bad condition as to 
be very disagreeable to walk upon. ‘They are greatly 
affected by changes of temperature, rapidly disintegrate, 
and are at best of but a temporary nature. 

Gravel makes an excellent footway pavement for sub- 
urban districts, parks, and pleasure grounds. If properly 
constructed and well drained, such pavements form, in such 
localities, pleasant and durable footways. 


1904. Construction of Natural Stone Foot- 
ways.—The slabs or flagstones should be not less than 
3 inches thick and of uniform thickness throughout; each 
stone should contain not less than 12 square feet of superfi- 
cial area; the top should be cut evenly, and the edges should 
be dressed square throughout the full depth of the stone. 
The flagstones should be laid upon a bed of sand or clean, 
gritty earth; they should be well bedded in the sand founda- 
tion and settled to a solid, even bearing. The joints should 
be closed with hydraulic-cement mortar. 


ELE PAVING. 


1905. Construction of Artificial Stone Foot- 
ways.—Several varieties of artificial stone are used; the 
process of manufacture is practically the same for all 
kinds, however, the difference being due to variations in 
the materials employed and proportions used. Portland 
cement, sand, gravel, and broken stone are the materials 
commonly used. When the stone is manufactured in the 
form of slabs at a factory, they are laid in the same manner 
as natural stone. 

When the artificial stone is manufactured in place in the 
footwalk, the process should be substantially as follows: 
The ground should be excavated to a depth of not less than 
8 inches below the intended surface of the finished pave- 
ment, and tosuch greater depth as may be necessary to 
secure a solid foundation and remove all perishable material. 
Where excavated deeper than 8 inches, the deficiency should 
be filled with suitable material, and the entire surface should 
be well compacted by ramming. Upon this natural foun- 
dation should be spread a layer of gravel, cinders, clinker, 
broken stone, or similar material, which should be well con- 
solidated so as to have a finished thickness of about 4 inches. 
On this should be spread a layer of hydraulic-cement con- 
crete, whose composition may be as follows: 


Materials. Parts by Measure 
American hydraulic: cemenitec: sien i 
DADC 9 cera a ay Stes eC pee ee 2 to 3 
Gravel-cand broken stones. ss6 ene dD to 


This concrete should be spread in molds formed of strips 
of boards about 4 inch in thickness set upon the gravel or 
cinder foundation and adjusted to the required grade and 
slope; these strips should also be placed along the outer. 
edges of the walk. In these molds should be placed the 
layer of concrete, which should have a thickness cf apout 
34 inches when thoroughly consolidated by ramming. 
After the concrete has set, it should be covered witha wear- 
ing coat composed of equal parts of Portland cement and 
clean, sharp sand; this should be from 4 to 1 inch in thick- 


PAVING. Tie 


ness, a3 may be required; its surface should be neatly 
troweled to the proper grade. 

After the concrete is set and before the wearing coat is 
spread upon it, the strips of wood used for molds should 
be removed; this will leave joints about half an inch wide 
between the blocks of artificial stone, which, in some 
processes are filled, and in other processes left open. 

The pavement should be kept damp by frequently sprink- 
ling it with water for a period of at least 10 days, and 
should also be protected from the heat of the sun by a 
covering of damp sand. ‘Travel should be kept off from 
the pavement for about 15 days, or until thoroughly set. 


1906. Construction of Brick Footways.—Selected 
paving brick should be used for footways; they should be 
of suitable quality and of uniform size and texture. 

For the best construction, a foundation of hydraulic 
cement concrete should be prepared, upon which the bricks 
should be set on edge in hydraulic cement mortar and their 
joints filled flush with the mortar. 2 

The more common construction, however, is generally 
about as follows: The ground is excavated to a depth of 10 
inches below the surface of the intended pavement, and as 
much further as may be necessary to obtain a solid founda- 
tion and remove all unsuitable material, the space being 
filled to the proper level with clean sand, gravel, or other 
suitable material. Uponthis foundation is placed a layer of 
fine, clean, sandy gravel, containing no pebbles larger than 
14 inches in greatest dimension, the gravel having a depth 
of not less than 4 inches when consolidated. After this has 
been thoroughly consolidated by rolling or ramming, a 
layer of fine, clean, sharp sand 4 inches in thickness is 
spread upon it to serve as a bed for the bricks. The sur- 
face of this sand bed is made parallel to the intended 
surface of the finished pavement and at a distance below it 
equal to a little less than the thickness of a brick. 

The bricks are laid flat upon this bed of sand, either at 
right angles to the line of the footway or diagonally in the 


1178 PAVING. 


manner known as the herring-bone style, the bricks 
being of uniform width and depth and so laid as to break 
joints longitudinally by a lap of not less than 2 inches. In 
laying the bricks, the pavers stand or kneel upon the bricks 
already laid, so as not to disturb the bed of sand. When 
thus laid, the bricks are immediately covered with fine, 
clean, sharp sand, free from clay, loam, or earthy matter; 
they are then carefully rammed by striking with a heavy 
hammer upon a plank placed over several courses. The 
ramming is continued until the bricks are settled to a solid, 
unyielding bed. When the ramming is completed, fine, 
dry sand is spread 
over the surface and 
swept into the joints. 
The plan of a por- 
? tion of a brick foot- 
way -laid’in \tias 
manner is shown in 
Fig. 440. It will be 
noticed that when 
the bricks are laid in 
this way a special 
triangular form of 
bricks is required to 
pages fit against the curb- 
ing at the sides of the footway, which is formed by bricks 
set on edge. 




















1907. Construction of Sheet Asphait Footways., 
—Sheet asphalt footways are constructed in about the same 
manner as the sheet asphalt pavements for roadways, 
except that the construction is of a lighter character. The 
ground should be excavated toa depth of 3 inches below 
the intended surface of the pavement, and to a greater 
depth where necessary in order to remove unsuitable ma- 
terial and secure a firm foundation, the deficiency being 
filled with clean gravel or other proper material; this foun- 
dation should be thoroughly rolled or rammed. 


PAVING. “1179 


Upon the foundation thus formed should be spread a 
layer of clean broken stone, to such depth that after com- 
pacting it will have a thickness of 2 inches. When this 
has been compressed by rolling and tamping, a binding 
material consisting of coal-tar distillate or distillate paving 
cement (Art. 1887) should be poured over it at a tem- 
perature of about 250 degrees Fahr.; about $ gallon of the 
binding material should be used to each square yard of 
pavement; it should be poured upon the broken stone in 
such manner.as to thoroughly coat the stones and fill the 
interstices. 

The wearing surface should consist of asphalt paving 
cement (Art. 1871), with which should be mixed crushed 
stone or crushed stone and sand; with this mixture may 
be combined a large proportion, of the cold asphaltic paving 
material taken up in repairing the wearing surface of 
asphalt pavements. The proportions should be about as 
follows: 


Material. Per Cent. 
ORES Seyi ta ate: | ee er oa 69 to 76 
VEN gata SA hi | Co Oe Ae a ae ieee tOeLD 
PASDUALC PavileeCRINe LO vidas 0s oes Sto 9 


The crushed stone should not exceed 4 of an inch in 
greatest dimensions, and should consist largely of stone 
dust. ‘This should be mixed with the old paving material, 
which should be broken into small pieces. The mixture 
should be heated to a temperature of about 300 degrees 
Fahr., the asphalt paving cement added, and the whole 
thoroughly mixed by stirring. It should be delivered upon 
the pavement at a temperature of from 250 to 275 degrees 
Fahr., and spread upon the base by means of hot iron rakes 
to such depth as will give a thickness of 1 inch after com- 
pression. » It should then be thoroughly compressed by roll- 
ing and ramming, during which process a small amount of 
hydraulic cement should be swept lightly over the surface. 


1908. Construction of Compressed Asphalt 
Tile Footways.—The compressed asphalt tiles used for 


1180 PAVING. 


footways are formed in nearly the same manner as the 
asphalt paving blocks (Art. 1881); the tiles, however, are 
usually 8 inches square and 24 inches thick. 

The construction of these footways is almost identical 
with the construction of brick footways, as described in 












































FIG. 441. Fic. 442. 


Art. 1906, and the description need not be repeated. Two 
methods of laying the tiles are shown in Figs. 441 and 442. 


1909. Construction of Wood Footways.—These 
are commonly constructed of pine plank 2 inches in thick- 
ness and surfaced upon the upper side, laid crosswise of the 
walk on wooden stringers 4 x 4 inches in cross-section; the 
stringers are laid longitudinally and bedded in the earth. . 
The construction is so familiar as to require no further de- 
scription here. 


1910. Construction of Tar Concrete Footways. 
—These are constructed in various ways. In one method 
the proportions of the materials are as follows: 


Material. - Parts by Measure. 
Steam ash OS x5 es tee ee ae nee es 3 
Portland:cemenvt sa eee eee is 
harp ‘Sanco sree ee toe ee eee eee 1 
Gas tare cee et ce cs, See a on nee Cte 9 


PAVING, 1181 


mhe ashes “sand) and cement ate mixed dry, then the 
water and tar added, and the mass mixed in the same manner 
as ordinary mortar. When thoroughly mixed it is passed 
several times through what is known as a pug mill, for the 
purpose of freeing it from a considerable portion of the 
water, which was necessary to the thorough mixing. It is 
laid on a prepared foundation toa depth of from 3 to 4 
inches, and thoroughly rammed and rolled. After the con- 
crete has set, a small quantity of clean, sharp sand is spread 
over the surface and allowed to remain three or four days, 
then removed. 

In another method, the materials used in the first course 
are as follows: 


Material. Parts by Measure. 
PO YL ECCT LOSE alto tc ein acess ciao ee aia 8 30 
EEE R AT eis lie bra cd era NS x tas ete odieka ave 29 
Reet ree oie cia AN Gk <ck05.0s oSiy aes Sie es 5) 


This mixture is placed ina layer 3 or 4inchesin depth and 
thoroughly rolled. Upon this is laid a coating from 1 to 
14 inches in thickness composed of the following mixture: 


Material. Parts by Measure. 
Cie Pe SUPE POP RSNES SCS oo So a eek Sete sur elt 30 
(Eo) ee pial Gea a es ge eS cal ae 30 
ae ete Getto ec alee hie eat eae 24 


The clinkers used are the rough clinkers from anthracite 
coal, or iron clinkers from a foundry. The materials must 
be thoroughly mixed and the layer of the concrete well rolled 
and then sanded. 


1911. Construction of Gravel Footways.—Gravel 
makes a veryexcellent footway pavement for suburban and 
country roads, parks, pleasure grounds, etc. 

The same principles apply to the construction of gravel 
footways as to the construction of gravel roads, the chief 
requirements being that they must be thoroughly drained 
and well compacted by rolling. The use of gravel as a road 
material, and the construction of gravel roads, were treated 


1182 PAVING. 


at great length in Arts. 1684, 1685, and 1691, 
and it will not be necessary to add anything to what is there 
given. Footways for pedestrians are, of course, of a lighter 
character of. construction than roadways for the passage of 
vehicles, but otherwise the construction of gravel footways 
may be considered to be substantially as given in those 
articles for gravel roadways. The floods of water from 
violent storms, which flow over the walks, washing out gul- 
leys and otherwise injuring them, is the agency that works 
the most destructive effect upon gravel footways. It is 
essential that the water from adjoining slopes be kept off 
from the footways, and that drainage be provided for such 
water as comes upon them. 


CROSSING STONES. 


1912. Where Used. — At street intersections, or 
wherever the footway of one street crosses the roadway of 
another street, in order to make the footway continuous it 
is customary to lay two or more rows of stone slabs across 
the roadway. For theconvenience of pedestrians, these are 
laid at as near the grade of the footway as circumstances will 
permit. Such stones are called crossing stonesor bridge 
stones. Crossing stones are generally laid at the street 
intersections in stone pavements, but are commonly omitted 
from the smoother pavements, such as asphalt and brick. 


1913. Size and Quality of Stones.—Crossing stones 
should be not less than 3 or more than 8 feet long and of 
uniform width and thickness; the width should not exceed 
2 feet nor be less than 10 inches, and the thickness should 
be from 6 to 8 inches; the top surface should be hammer- 
dressed, and the ends should be dressed square the full depth 
of the stones, so as to form close joints. <A suitable quality 
of sandstone is the best material for cross stones; it is supe- 
rior to granite for this purpose, because its surface does not 
wear smooth and become slippery, as granite does. The 
manner in which crossing stones are laid will be understood 


PAVING. 1183 
from Fig. 443, which is a view of a portion of a street inter- 
section, showing the crossing stones; f is the wearing 
surface of a granite-block pavement, g is the gutter, # is the 



















































































































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resgopthign 3 Twelve fthts. Two of this. pezestecghc. Oneal: OneLefe._ wo ofa 
JUNE 25, /893 Copyright, 1895, 1897, by THE COLLIERY ENGINEER COMPANY. All rights reserved. TOFLN SMITH, CLASS N° 4529. 
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Copyright, 1895, 1897, by THE COLLIERY ENGINEER COMPANY. All rights reserved. 


JUNE 25.1893. 








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Oven ANY PAGES 


CONTAINING 


TABLES AND FORMULAS. 


COEFFICIENTS FOR ROADWAY -CROWNS.* 





—_—— 





Value 

Character of Roadway. of ¢. 
Common earth roadways...... | zy 
Ordinary gravel roadways.....| 35 
Broken stone roadways....... bale 
Wooden block pavement...... dy 
WCopblestone pavement......~. ay 
Granite block pavement....... | sty 
Well-laid brick pavement..... isa 
First-class asphalt pavement..| 7+, 











* This table gives the value of g in the formula 


sip p(i0g — 1) 
eset E 800 








in which c is the amount of crown, w is the width of the roadway, and 
f is the per cent. of grade. 


INGREDIENTS FOR ASPHALT PAVING 


MATERIALS. 

Material. Per Cent. 

(1) 
PB UA LUV CECI LGRE Cenc teri ee # <f'<)e isn, « 12 to 15 
cor Vi UR as, aa Ae ee 83 to 70 
Puiverized carbonate of lime... ... +. FetO: 1s 

(2) 
Bt UAC OC TIEN Derwent i ood ten ae 13 to 16 
SRL. SRE ER RE oe ee ores ee 63 to 58 
Bah etal ERM eM Ra cckaty ty cand sous 28 to 23 


Pulverized carbonate-of lime i... +... a dies & 


aE, 
Ow 


TABLES AND FORMULAS: 


INGREDIENTS FOR HYDRAULIC CEMENT 


CONCRETE. 
reteral, pe oye 
Measure. 
(1) 
Natural cement. eee I 
SOT, seg ee 2 
Broken stone: 2 S.c5. as aaa ee 3 
(2) 
Portland cement. -> a. oo eee ee I 
Sand. 252 igs ee se ee cone a s) 
Brokenstone ay est tek ice ee 7 
(3) 
Pértland cement 2 2 ee eee I 
DANG Jo sess yb ae one lee ee ee ee 24 
Gra Velie ois 65h IRR eae cetera coe ee 3 
Broken Stones.“ ek eae ee eee 5 


TABLES AND FORMULAS. . 3 


RESISTANCE TO TRACTION ON DIFFERENT 
ROADWAY SURFACES. 








Resistance to Traction. 


In Pounds per Gross Ton. 

















Character of Roadway Surface. ferrerns 
of Load 
Maxi- Mini- | Pa 
mum. mum. lt 

Earth (ordinary) Ren te oe 300 125 200 ar 
Earth (dry and hard)....| 125 iio 100 sis 
Gravel: (COMMON), © 50. 147 140 143 ar 
Minvelthard- rolled): 6. .2 pie 75 hy 
Macadam (ordinary)...... 140 60 go ay 
Matadam (G00) v.22... 80 4I 60 ar 
Macadam (best) s?.2..%.". 64 30 50 ar 
Cobblestoneé*(ordinary)/4) ss. Puan 140 ae 
Cobblestone (good)....... Pars ve i 75 gly 
Granite block (ordinary).| .... aPar go se 
Granite block (good) .... 80 45 $67 }. a. 
Granite block (best) ..... 40 25 34 ae 
Belgian block (ordinary)..| .... Fash 56 Jy 
Belgian block (good) .... 50 26 38 = 
HATE Oar Rtas, ioe eed 56 32 44 ahs 
Wooden block (in good 

OATCL LOTR gens o's ais 40 20 30 alg 
JRE OTE WS) og eee er 39 15 22 aid 








INGREDIENTS FOR DISTILLATE PAVEMENTS. 


Material. Per. Cent. 
Sa Gps en Te ela ts S cr ety dw 4 Sa 63 to 58 
Pore Stone OF LOCK OUSt .6 a ayy is >< 26.10 23 
Dtetiliateapavine .cement. <5 ce. cue Tato 15 
eee Te COMIC or errs «estes on = it 1, 90 
PlOseer mer och sivean af cite oahe Ss 0.15 


A Los Ramet PL ISE YL Caentel ea ehat ait aiorsi os pask ee «5 0.10 


4 TABLES AND FORMULAS. 


CRUSHING RESISTANCE OF DIFFERENT 
PAVING MATERIALS. 











Resistance in Pounds per Square Inch. 














Material. 

Minimum. | Maximum. Average. 
Graniter anaes Sees 5,300 35,000 £9,000 
Trap-1GCkis 2.72. eee 19,700 22,300 21,000 
Sandstotes..) ease ee eee 2,200 42,800 10,600 
LimeéstGn eosin eeoeeee 3,600 16,900 9,200 
Brick, "paving. ..eee ee 7,000 18,000 9,000 
Bricks commons) fee I,C0O 12,000 3,400 
WiGGd eis: 5s ee 2,900 19,000 7,000 























SPECIFIC GRAVITIES AND ABSORBING CA- 
PACITIES OF PAVING MATERIALS. 

















Material. Specific Gravity. pacaetnaiiman 
Granite cto wnt, cee 2.60 to 2.72 7 1sto meobG 
Limestone@... i. ss 2A Ost Or 27 5 5.00 tO .200 
DANCStone nes. DRT Cee ais 6.80 to 2410 
Bricks payin? en pee 1.90 to 2.70 7.00 tO .140 
Brickcommon..ca ee 1.50 tO 2.00 25.00 to 2.000 
WOO. cehoe ect om Beas £34 COs se 9.00 ton) #16e 
ASpnalit eee ees .goto 1.80 | Nearly impervious 





eo ee eee 


INDEX 


LA PAGE 
Abrasion, Tests for. s ; 1130 
Absorbing capacity of paving ma- 
terials . = - : . 1132 
Accuracy of dead toad : 1060 
Additions to cities . ‘ 1047 
Adjustment of grades at curb 
angles. ; 2 4 ‘ 1073 
Adverse possession . ‘ ; - 1098 
Aggregate and matrix . ‘ ae tlao 
Alinement of roads. ; : - 999 
Alternate stresses, Latticing of 
members subject to 857 
ih stresses, Provision for, 
by Cooper’s specifi- 
cations r * . 825 
Anchor bolts, Position of - . 1016 
HS bolts, Size of . ; .» 1016 
= bolts, Specifications re- 
lating to . " + gor 
4 bolts, Various forms of 1016 
Anchors, Specifications relating to gor 
Angle of repose ; f 1008, 1106 
Angles in tension, Connection of . 815 
xe Maximum and minimum 
weights of : ° 2. .830 
Area, Gross and net A . 854 
* Increase of, to provide pe 
bending stress . ; se ORT 
“ Increase of, to provide for 
wind stress . A x ae Beye 
‘“« “Minimum, of lateralrods . 816 
‘ ~of bridge member, Determi- 
nation of y 815 
* Reduction of, at poe 
required of steel 811 
“Reduction of, by rivet holes 81s 
Arrangement of floor joists . 862, 1045 
oS of rivets . 924, 941, 946 
Asphalt . A é ; - 1135 
Ee Bermudez . F : Heda 
“block pavements . Fe eet 
at gutters A : - SeLLIOX 


PAGE 
Asphalt, Lake and live . . <) 2154 
= pavement on railways 1162 
ne pavements - . 1154 
ot: paving cement. 1158 
*. Rock ; eer S5, 5rOs 
as Rock, pavements . an £163 
oy Sources of supply of II54 
Asphaltic cement ‘ 1140, 1158 
Asphaltum (see also Asphalt) 1136 
id paint . p : - 1077 
on pavements 1154 
a Refining of 1157 
Attachment of hand-rai! nosts . 1074 
Avenues . 5 ‘ : : . T1045 
Axle friction . ‘ 1101 
B PAGE 
Back wall of bridge. . . 1045 
Balanced section : ‘ pane O42 
Baltimore truss, Desarvipton of 778 
= truss, Stresses in, graph- 
ically determined 779 
Barbed bolt 2 : A é 1017 
Basalt : , : ; mxrrga 
Base, Bituminous, for asphalt 
pavements . ° T156 
as Ctty = d 1088 
Ss Concrete, for pavements . 1143 
whe Hydraulic, for asphalt 
pavements 1156 
Batten plates, Design of 945, 950 
a plates, length of, Estima- 
ting the 1057 
se plates, Pitch of rivets, in 946 
oe plates, Specifications re- 
lating to . : : 300 
Batter braces . é s A - 687 
Beam, Bending moment of . 884 


nA flanges, Pitch of rivets in 967, 971 

ss overhanging both supports, 
Uniform load of 7 

we hangers, Designof . E 


IOIO 


998 


Xil INDEX 
PAGE PAGE 
Beam hangers, Double . 1067 Bolts, Anchor . ; : : oe LOL 
de hangers, Ordered length of 1039 ‘SS Trectian. : i 4 - 1052 
a hangers, Plate 1067 &  SBormsror 1017 
hangers, Position of 973 ‘* for wheel guards, Naber 
ae hangers, Single . 1066 and size of . 1049 
se hangers, Specifications re- “ Shearing and bearing 
lating to 89g stresses allowed on 897 
zs hangers, Stiff . ~1069 ‘* Specifications reiating to go2 
se hangers, Weight of, used Boulevards ; : at 1071 
in estimates . 1059 Braced portal, Stresses in 795 
Beams above cherds 1066, 1069 ~=—s Braces of truss . 687 
os below chords 1066 Bracing, Specifications yalnteae is goo 
Bearing stress on pins ae 932 Brackets, Sidewalk . 798 
a stress on pins, Determi- Brick pavements 1170 
nation of . 915 Sean ii 1137 
os stress on rivets . 897, 921 “ " Size of paving 2. eYIGs 
be stress on rivets, Determi- Bridge, Classification of foaae on. 690 
nation of . 920 oe Deck ; , 687 
es stress on timber 876 ee floor, Weight of. < 700 
Bedplates, Design of IO14 a Half-deck . - - 688 
Be Specifications relating ie High-truss . 688 
to Fs ‘ : oe POOL ce Low-truss ; : 688 
Belgian block 1135 e Pin-connected . : - 688 
i. block Pvanicnte 1142 we Riveted : : 689 
Bench mark, Primary : 1089 oe seat 1045 
Bending moment due to weight of ee Through OST, 
beam 883 ay Truss, arch, and suave 
es moment in el Bast ace sion, distinguished 685 
to wind pressure 851 Broken-stone roads. 1025, 1033, 1038 
ae moment in floorbeam 728 st stone pavements 1146 
es moment in floorbeam Burnettizing timber 3 : a LIES 
with sidewalks 799 
be moment in pins 927 
= moment on shoe plate 1009 C PAGE 
Be moment, Position of load Camber . : A = 2 + 903 
for maximum 802 ee Effect of, on length of 
* moment, Stresses due tb 735 diagonals . ps : 905 
re stress allowed on pins 897 ‘S Increase of panel (eneen 
te stress due to weight of to provide for , 4 + NOO4 
member . 880 “A Specifications relating to go2, go5 
i. LESE ear. - 809 a Usual amount of 904 
Bill of iron ; 1034 Camel-back truss . ;. ; 1 775 
‘of lumber . ; 1044, 1053 Cantilever truss 5 x 686 
** Shipping 1048 Capacity of bridge . : Ae telirers: 
Binder course 1157, 1168 Cast iron, Use of, in bridge wore: 807 
Bitumen ; 1136 Cement, Asphaltic . s Ap enh obra ots! 
Bituminous base foe BETA pave- cS Bituminous PR erie «, £E40 
ments 1156 . Distillate paving 1168 
Bs cement 1140 Center of gravity found by mo- 
: limestones 1135 ments : : : - 882 
‘e sandstone . ; 1135 Channels, Distance between, in 
Block, Belgian . F : LLL chord sections . 827 
as corners. 1080 ha Formula for width of 
Blocks, City 1042, 1044 flange . ‘ 833 
‘* ‘Expansion be , . 1152 * Maximum and mini- 
“  -Paving (see Paving Blocks) mum weights of 5 EES 


INDEX 


PAGE 
Check-nuts ‘ é : : - 999 
Chemical treatment of paving 
blocks. ; : ‘ : 
Chord stresses, Formula for, in 
Howe & Pratt trusses . 762 
stresses, Formulas for, in 
inclined-chord and _ di- 
vided panel trusses . 768, 781 
stresses from wind pres- 
Sure = 3 4 5 Ole 
Chords, Curved : : ; ~ 750 
a Effect of wind stresses on 850 


1152 


ch 


66 


Inclined ae a ; 750, 764 
ve Lower, Design of 818, 979 
*“* ‘Upper . . 833, 948 


if: Widthof . " : a 760 


City base . ‘ : : , . 1088 
. aatum : ; ‘ é 1088 
Clay 5 ; ‘ : ; : - F137 
Clearance between eyebars . a OT 
if General rules relating 
BO. . ° : Ore 
a of pinholes. : . 899 
Clerk Maxwell method for the 
graphical-+determination of 
LVesSeS\ s . . ‘ - °733 
Goals tar" ©: } , ; : eee +s: ee 
>. tar pavements : « 21954,.1167 
Coat, Cushion (see Cushion Coat) 
Cobblestone pavements . II4I 
Coefficient of elasticity of struc- 
turalsteel , - A ee 
eb OL Aex pa hsrons of 
wrought iron and 
steel . ; ; 3, LOOT 
a of friction. : . 1008 
As of friction. of wrought 
iron, steel, and ma- 
sonry ; : ap. eyo 
‘ of rolling friction 1103, 1107 
Cold-bending test. : , . 809 
Columns, Formulas for unit stress 
allowed on . ‘ . 824 
i Length of : ene 
43 Rankine’s formula for 
resistance of : i > B83 
Compression mein bers F Hy ee 
3: members, curve and 
straight line, For- 
mulas for - 823 


eS members, Length of 825 


ms members, Propor- 


tioning of 826, 833 
ee members, Symmeét- 

rical and unsym- 

metrical , . . 1084 


Xill 


PAGE 
Compression members, Unit 
stresses allowed on 824 
members, Usual 
forms of . : . 819 
Compressive stresses, Formulas 
for, based on fa- 
tigue of metals . 873 


cs stresses, Formulas 
for steel. . 869 

* stresses, Formulas 
for wrought iron 822 
Concentrated loads cA . 690 
ae wheelloads . ab COG 
Conerere, * “ : : . A) ails. 
Connections, Strength of 4 .- 897 
Construction of pavements . meet iat 
" of roads °. 4 <2 Ose 
Continuous truss, i = <  8eC 


Cooper's specifications for highway 
bridges . : : 5 i » 869 


Cost of pavements 1118, 1128 
Cotter pins ; , ‘ : 1023 
Be pins, Dimensions of . . 1024 
a pins, Grip of : : . 1024 
Counter stresses, When, are in- 
duced : ; - : , ~  7oo 
Counterbraces . : : : - 687 
he Design of . 987, 992 


“ 


When, are required 711 
Countersunk rivets . 
Country roads (see also Roads) 
pe roads, Difference be- 
tween, and city streets 95 
Course, Binder , 1157, 1168 
Cover-plates, Maximum width and 


1083 


thickness of , : # Ges 

he plates, Pitch ofrivetsin . 41 

af plates, Width of . ; ONE Se: 

Covering capacity of paints . - 1079 

Creosoting of timber F : 5 ELSS 

Crossing stones ; : - . x182 

Crown, Curving and sloping . «. 1059 

Me Eccentric . ; : S =i1070 

. of roads : : A 1018 

es of streets. é ; +). 1057 
Crushing resistance of paving 

materials é : . ~ phrgt 

Curb angles ; : » f « 1675 

a COrners. ‘ FS - 1072 

Curbing, Construction of 4 . 1172 

=) Height of . : : . 1066 

Curve formulas for columns , » 023 
Curved chords, Graphical deter- 
mination of stresses 

yng x : A 50 


«© chords when used ... 749 


xiv’ INDEX 
PAGE PAGE 
Cushion coat for asphalt pave- Design of compression members 826, 833 
Tents ee : : 1160 — ,OL Counters: s 4 987, 992 
se coat for brick pavements 1171 ‘of diagonal members 986 
coat for stone pavements 1143 = of end post . 833, 941 
oe coat for wood pavements 1149 os of floorbeams 859, 966 
es of intermediate posts 951 
D PAGE o of knee braces 964 
Data of bridge . : : : “2 O05 Ys oflateralrods . é Qg2 
Dead load . ‘ ; : 690, 704 * of lateral struts . 838, 963 

‘* load, Approximate formulas = of lattice bars 845, 958 
for calculating 705 si oflower chord . 818, 979 

“load, Difference between oh of pin plates 914, 944, 980 
assumed and final 1060 Oy of pins . 912, 931, 936 

*“ load, Distribution of, be- Me of portal Beaches: 842, 958 
tween upper and lower ix of shoe strut 848, 965 
chords . 707 ss of tension members 817 

** load of bridge wit th Ss tee - A of tension web members 986 
walks 798 ek of ties °. : . 986 

** load stresses 7) of upper chord 833, 948 

** load stresses for, wrodete, ce Practical hints concerning 1087 
iron compression mem - Detail drawings, Natureand useof 895 
bers (Cooper) . 824 #&Details of floorbeams 966 

** load stresses for ae ne My of specifications, Relating 
iron tension members to : 897, 902 
(Cooper) 814 Diagonal Serpe ies Calculation of 

‘* load stresses, Grouioal ae exact length of 905 
termination of, in Balti- ru members, Design of 986 
more truss . : : 77 S members, Economical in- 

‘* load stresses, Graphical de- clination of . 5 749 
termination of, in Petit Diagram, Erection 1053 
truss : 787 Dimensions of nuts. : Ar falels) 

** load stresses, Graphicn es ee of timber floor aeiceae 865 
termination of, in truss Distillate pavements 1167 
with curved chords 751 mi paving cement 1168 

‘* load stresses, Graphical de- Divided panel . = . " ee 77 
termination of, in truss Dolomite . ; “ 1135 
with inclined chords . 765 Double beam aeteer 1067 

*““ load stresses, Graphical de- oo intersection or aa ah te 
termination of, in truss quadrangular truss 774 
with parallel chords . 707 Drainage of roads IOTQ, 1031 

** load stresses, Graphical de- Drawings, Detail and working 895 
termination of, in Whipple oc shop, Data given on 1026 
truss E ; A oS Durability of pavements 1116 

Deck bridges 687 

“bridges, Ticeepntion of dana E PAGE 
load between chords of 877. Earth roads . 1030, 1035, 1038 

‘* bridges, Minimum stress in Eccentric crowns at street inter- 
center strut of ome Ow sections : 1076 

“bridges, Stresses in 711, 715 Eccentricity, Newatiog ; ; ». O07 

Depth of floorbeam Nay 5) wi Neto ‘ : ~ 887 

Ee. tess 749, 862, 871, 875 Ht of pin plates . 1084 

‘** of truss used for lateral sys- ss of pins é : - 886 
terse. ; 712 4, of section. . a a) ROS 

Design of batten plates 945, 950 = of stress, Iiffects of . 881 
of beam hangers. 3 GOS Economical form and height of 

3 of bedplates - - » 1014 bridge truss . A ° ° ° 749 


. 


INDEX XV 


. PAGE 
Economy of pavements . ‘ ve TL, 

Effect of wind on chords and end 
posts : 815, 850 
Effective depth of dcacient S730 

Elastic limit of structural steel in 
general. . 811 

= limit required by eieciticn: 
tions for steel . OLS 


a limit required by specifica- 


tions for wrought iron.. 809 
Elongation reauired by specifica- 
tions (steel) ; i 9 Sic 
required by specifica- © 
tions (wrought iron) 809 


“ec 


Encroachmert of lines . 3 - 1097 
End posts, Correction for wind 
stress 815, 850 


‘* posts, Design of 833. 941 
Erection bolts, Use and dimensions 


EY a: " . 1052 
“ * diagram, Ratitre ted uses 
CFS ‘ ; eV L053 
Error in determining maximum 
web stresses - . 2 P 793 
Estimates of weight of epitartal, 
Making . ‘ 5 - 1054 


Expansion, Coefficient of tor 
wrought iron and 


steel . . 1007 

*s in bridge work, Peovts 
ding for : + QOT, 1007 
He of paving blocks . pe xa 
Be rollers, Design of . 1005 

Ke rollers, Specifications 
relating to . ; . ~ OnE 
External forces intruss . A . 685 
Eyebars, Clearance between - 937 
ra FHeads of . “ s 899, 975 
F PAGE 
Fatigue of metals, Cause of . . 872 


he of metals, Formulas for 
unit stresses founded on 873 
Le of metals, Importance of, 


in structural work. : 9873 

Ss of metals, Requirements 
Ota : : : ¥ hess 

“a of metals, Specifications 
foundedon . F 874 

Ah of metals, Woehler’s fae 
relating to A . . 972 
Fiber stress x 5 : - poh: 
Field rivets : ‘ A F . 1048 
Filler rings, Uses of ; : 3. LOze 


Final pitch of rivets, Determina- 
tionof . . s . ° Ag Gteye 


PAGE 
Fixed load ‘ ; ; - 690 
Flange stresses in Haas renin: For- 
mulafor . 2 ; oe ese. 
stresses in portal, Deter- 
mination of 721, 725 
Flanges of channels, Width of Ae tier: 
og Pitch of rivets in 967, 971 
Staying of . F : 875 
Flat-ended columns, Require- 


se 


ae 


ments. for ‘ - : ‘ . 1086 

Floorbedm hangers 998, 1066 

“stresses ‘ : - 726 

Floorbeams . - 7 . = 720 
eg Bending moment at 


any pointof . - 728 


cs Design of 859, 966 
“5 Effective and _ total 
depthof . : 730 
# Formula for w Stefi 
of : “ - 927 
ke Maximum dines 
stressin . z © 73° 


Maximum shearin ., 731 
Position and connec- 


tionsof  . : 1066 
Ly Shear at any point of 968 
vs Weight of, used in 
estimates. : - 1058 
_ with sidewalk canti- 
levers : ; - 798 
Floor, Details of ; é - 0966 
‘© joists, Arrangement of 862, 1045 
y joists, Dimensions of . « 865 
‘* = joists, Metal . 1062, 1064 
‘* joists, Stresses allowed 
on . - ‘ : «) 863 
I WeIritc Or. ° : - 706 
Footways, Artificial stone * £176 
os Brick : P . 1297 
Compressed Eeaeai te 6 2. 
+ Details of ; ~ Shey 
re Gravel . : a EEOE 
“ Natural stone - axis 
*S Sheet asphalt 7 + 1178 
e Tar concrete . , < Tico 
ss Wood - ‘ : - 1180 
Forces, External 5 - 685 
Forked ends, Specifications get 
Cins ty A : " . <2) -G00 
Foundation for asphalt pave- 
ments ‘ . 13156, 1164 
s for block-asphalt 
pavements. - 1166 


for brick pavements 1170 
for coal-tar or distil- 
late pavements . 1168 


Xvi INDEX 
PAGE . PAGE 
Foundation for granite- block Graphical determination of 
pavements Tras stresses in inclined 
os for wood pavements 1147 chords . : 765 
Foundations of roads 1032 -t determination o f 
Friction, Axle IIOL stresses in lower lat- 
te Coefficients of, for ateeh eral system . 711, 715 
wrought iron, and ma- y determination of 
Ssoury,) - 878 stresses in Petit truss 787 
es Coefficient of rollin 1103 o5 determination of 
oe General law of ; SeeLTOS stresses in Pratt 
Rolling. 5 ‘ LeeLIOL truss 694, 707 
s¢ determinations ot 
stresses in Warren 
G PAGE girder? * .6t jos, pee 
Girder, Latticed : : ; . 689 Graphite paint . , : ; . 1078 
* Plate. - cee OSG Gravel roads 1028, 1034 
“plate, Effective Gepen: of . 859 Greenstone ; ‘ : : ek 
‘¢ plate. Minimum thickness Grip of cotter pins 1024 
of web of . P 3 . 859 ‘* of pins, Determination of 1018 
Me plate, Stiffening of . - 850 Gross section . 4 : = Ose 
‘© plate, Thacher’s specifica- Gutters . “ : : ° . 1064 
tions relating to . . 875 ©) <Aspitalt: : : & © vee etos 
+ Riveted 5 : ; - 689 
Neb 3 ea also cures E H ace 
a eae sae A Ae ce Half-deck bridges . 4 ; . 688 
* a hi si “ae Mee ‘hitch ‘truss; ) =n (oe ee 
‘ cae ee on hig des 999, 100 Wandhocte ‘ i os ee 
e of a a pray ees ee Hanger plates, intercon: of + LOO, 
Sapa St ak ap a ea Headroom, Amount of, in 
ei f pt aba di 9% bridges . < - . 862, 871, 875 
rr 4 ne: 705° Heads of eyebars . ; 890, 975 
i ER , 7 ae High steel, Properties of, required 
A record 1087 * ake 3 
\ i tetion a y specifications. ; II 
xm) eg da ieee ; . 4 “steel, Weight and spenine 
es ne ae blishin “ : ‘ ets gravity of rolled sections of 878 
radi en g if ; eh aes ““ truss bridges . : : - 688 
oo dots ae peyrns ‘ ge Horizontal component of chord 
eee : _ = Sabet stresses . - ihe 763, 781 
ra block easement 1143 
Horses, Tractive shwer OLamar 1108 
Gr aphical determination of avel H 
owe truss s é F F se aTAr 
load stresses in truss % 
f truss, Formula for chord 
with parallel chords . 694 ? 
Z : é stressesin . : : ~ 762 
“ determination of maxi- ie ° : 
; truss, Stressesin . : Ae “ozs 
mum stress in chords ~ 697 #5 : 
: ; ; truss, Where, are advan- 
2: determination of maxi- 
: tageously used . . TAT 
mum stresses in web H 
seen ae ub guards 3 1071 
pee : 3 7 Hydraulic base for apeaty pave-. 
on determination Gr 
CNTs aa : - s : 1156 
stresses in Baltimore 
truss 779, 782 
determination of is PAGE 
stresses, Clerk Max- I beams 1062 
well method : - 933 i. beams, Piopertich of “Carneos 
i. determination of steel : : : . 1064 
stresses in curved I beams, Sirenati of 106 
> 
chords. & : - g5t Imperfectdesign . - : - 1082 


INDEX 


PAGE 
Inclined chord . ‘ aaa tee 
Inclined chords, Formulas for 


stressesin  . A 763, 781 
“ chords, Stresses in truss 
having 765, 768 
be chords, Use of . a TAG 
Initial stresses in lateral rods, 


Treatment of 825, 838 
Intermediate posts, Design of 833, 841, 951 


Intersections, Street 1071 
Iron hub guards 2 ; : + 1072 
* order : 7 - a eerOys 
‘““ order,how made ., « 1035, 1042 
** “oxide paint , - A - 1077 
J PAGE 


Joint filling for pavements 1144, 1151, 1171 


Joints, Splicing 5 : - 898, g50 
<s Strength of . : ; Se o7 
Joists, Arrangement of 862, 1045 
==) Dimensions of: y on 805 
‘Metal ; = “ - 1062, 1064 

‘* Number of linesof  . 2 | 865 

‘“* Stresses allowed on . <a 308 

K PAGE 


Knee-brace, Design of . ~ = OOF 
“brace, Length of, used in 
estimates 


1057 
Kyanizing of timber : : “y Sbace 
L PAGE 


Lacing, Definition of 4 c $3" 946 
Lateral rods, Connections of . 949, 973 
ee rods, Design of . . -  9g2 
rods, Initial strain on . 825 
rods, Minimum areaaf . 816 
slope of streets 1078 
a: stresses : : .- 760 
struts, Designs oF 838, 963 
struts, Stress assumed on 825 
wf struts, Stress in, due to 
initial stress in lateral 


rodsa. : - 839 
? system, ieacher ant: a ae 

to chords ane goo 
oF system, Depth of ts uss 

used for . ‘ - 72 
che system, Minimum Sinus 

in center strut of . - 761 


system, Panel length of, 

in truss with non-paral- 

lel chords : : 761 
* system, Pratt truss type of 761 


XVil 


PAGE 
Lattice bars r : . - - 946 
ee bars, Design of . a 845,958 


te bars, Dimensions and spa- 


cing of 946, 948, 954 
ss bars, Estimating the length 
of : % : 2 we) EOS7 


ve 


barsin tension members . 857 
bars, Ordered length of 1039 
ak bars, os Naa rela- 
ting to - &99 
bars, Stresses in ae of 
portal P : a 3 725 
Latticed girder ; : ‘ <P eisto 


“ce 


Lawns, Street . ; @. 1069 
Length affected by riaholes 5 . 907 
Me changed by camber . «Be GOK 

cs Maximum, of compression 
members . : ; >» ») ae5 
* of pins . 1037 

a of various members, Esti- 
mating the ‘ ; » 1055 

ie Theoretical, of bridge 
members . : - . 825 
Lewis’s specifications . : . 877 
Life of pavements : 1116 
Light weights . - . : - 1083 
Limestone. ; 1134 
3: Bituminous 1135 
Limitation, Statutes of 1098 


Limiting values of pitch of rivets 808, 964 
Line of action of stresses in mem- 


bers. P ; : - 687 

Lines, Hacpoanhinesk of. : - 1097 
‘* street, Marking and per- 

petuating : 1089 

Live chord stresses, Maximum  . 6094 

“load =. ‘ 600 
‘* load stresses a v1 lowe a es Vv 
Cooper's specifications for 

wrought-iron members 814, 824 


load stresses, Graphical de- 
termination of, in truss 
with parallelchords . + Aood 
load stresses, Graphical de- 
termination of short method 737 
load stresses in Baltimore 
truss ‘ 782 
load stresses in fchetda fad d 
from dead-load stresses . 753 
load stresses in Petit truss . 789 
load web stresses, Maximum — 699 
load stresses in truss with 
Ur y Cul Omen crined 
chords 753, 768 
load stresses in Whines 
truss : . F : « 1776 


XVill INDEX 

PAGE PAGE 

Load, Concentrated ‘ A A siete) Maximum stresses in chords, Con- 
Dead ; ; . 690 dition of loading for 694 

“ “Bffect of diginbution of, on a stresses in) chords: 

stresses inmembers . eo 604 Graphical determina- 
Loads, Moving . c : * — 6go0 tion of . ; : 697 
| “PAGS wee : ne. a . * Gor - stresses in deck pridees 715 

‘* Position of, for maximum Es stresses in diagonal and 

bending moment . - 802 vertical members of 
ey Unione 3 A - - 690 Pratt.crusse. P 700 


+ Wheels 4 : : ae. aaletsye: 
us Wind . ‘ : : - eo 


Location of city streets . ‘ - 1040 
oe: of highways G97, IOI 
se of highways and rail- 

roads compared . 7h 008 

Lomas recessed nut : : » . 102T 

Loops of bars and rods 987, 1037 


Lots, City : ; 4 1045 
Low-truss bridges . 3 “ - 688 
Lower lateral system, Graphical 


determination of stresses in 7Ily 715 

Lumber, Bill of 1044, 1053 
= Usual sizes carried in 

stock ; : ° LOnd 

M PAGE 

Macadam pavements - . set tAO 

ts roads A - ; 1025 

Maintenance of highways 1037 

a of pavements . + L126 

Map of highway road 1016 


Materials, Absorptive capacity of 


paving. : : 1132 
ue Crushing resistance of 

paving. 1131 
a Ordering 1034 
“e Sizes of, carHedin aoe IO4I 
‘ used for pavements 1129 
es used in bridge con- 

struction. 2 2 COT 
ee used in bridge con- 


struction, Selection of  8o2 
Matrix and aggregate 


II40 
Maximum and minimum wolehts 
of channels . ; %, 1030 
O bending moment, Posi 
tion of loads for - 802 
: Error in, from assump- 
tion of panel concen- 
trations ‘ : 7S 
* length of compression 
members. goes 
&¢ live-chord strevcee - 604 
eo load web stresses . : 699 
es shear in floorbeam a e7at 


stresses in Howe ioaes 742 
stresses in web mem- 
bers, Graphical deter- 
mination of . : : Joa 
stresses in web mem- 
bers, Short method 
for . A ; ne VEY 
Medium steel, Properties of, re- 
quired by specifications 811. 


2 steel, Unit stresses al- 
lowed on d - 869 

Members, Convenient and limiting 
dimensions of . 28 WSOE 

, Exact length of diago- 
nal ; Z ; ros 

pe Line of action of stresses 
ine cl : - a OOF 

< Maximum and mini- 
mum dimensions of . 825 

My Stresses in, affected by 
distribution of load 692, 694 

“e Tension and compres- 
sion “ . 686 
oe Theoretical length ef « 825 
Metal floor joists. Z . Ic62, 1064 
Metals, Fatigue of . ag Es ore 
Mineral pitch . A : 1136 
Minimum area of lateral rk: ES 
zs diameter of pins 899, 1020 

. thickness of web of gir- 
der 7 : - - 859 
Modules section . : si - 1063 


Modulus of elasticity . < . 80x 
Moment diagram, Determination 
of stresses by : 733 
Moments, Principle of, ee ohed KG 
determination of stresses in 
braced portal 5 F 4 - 796 


Monuments for street lines . « I0Q1 
Moving load. : - - «4660 

N PAGE 
Nails, Dimensions and weights of 1050 
Name plates. : “ : LOL 
Negative eccentricity . : - 887 


Net eccentricity 4 - ‘ . 8O7 


INDEX X1X 
. PAGE PAGE 
Net section of bridge members 815,884 Pavements, Safety of . TII4 
Wats, Check  . 3 : 699 bs Sandstone-block sen ht 
‘Dimensions of : - 994, 996 iS Tonnage of traffic 
‘* Lomas recessed . s = tO2T over . 1124 
See Pilot oe - ; IOIg py Wood . 1147 
“ Standard aps: 9099 ~=@ Paving blocks, Asphalt . 1165 
cis blocks, Chemical treat- 
O PAGE ment of ‘ . r1g2 
Order list, Making an 1034, 1040 oe blocks, Expansion of. A pee 
urdered lengths of materia. 1035 = blocks, Granite 1144 
“ blocks, Sandstone 1145 
d PAGE Y blocks, Wood 1149 
Packing rings, Usesof . : + 2025 Petit truss, Description of 786 
Paint, Asphaltum ,. A ~ 1077 * truss, Graphical determina- 
‘* Graphite : = : - 1078 tion of stresses in 787, 789 
“* ion-oxide . : 1077 Pilot nuts : 1019 
*“* Red and white-lead : 1076  Pin-connected bridges 688 
Painted surface, Amount of . . I080 ** connecied bridges, Use of 877 
Painting of bridges 4 * +. 2675 ** -pilot, Use of : 1020 
Preparing iron for . - 1081 ‘* plates, Design of 914, 944, 980 
Paints, Covering capacity of . - 1079 ‘© plates, Dimensions of 024 
Panel F : ; . 686 ‘* plates, Eccentricity of 1084 
‘* concentrations P ‘ s 60% ‘** plates for tension members, 
** concentrations, Error arising Metal behind pin in 983 
from assumption of . ft sa ““ plates, Strut resistance of 936 
eT ided: : ; : Sey i 5 ‘* washers, Description and uses 
‘* Increased length of, to pro- ef? ~ é : 1025 
vide for camber go4 Pinholes, Clearance of 899 
i lesigths: —. : ; ‘ 686 be Reinforcing plates in goo 
= load. : : . : 691 Pins, Bearing stress allowed on 897, 932 
** load, Determining the 691 *“* Bending moment on 927 
Patks:. = ; ‘ 3 s rose ‘* Bending stress allowed on 807 
Pavements, Asphalt, for railways 1168 “Clearance of . 899 
Bo Asphalt block 1165 * Computation of bending mo- 
ss Asphaltum . Lrs4 men on : ; * 027 
a Belgian-block . 1142 ‘* Correction in size of, to pro- 
f Brick ; 1170 vide for wind stress . . 929 
a Broken-stone . reat ‘* Determining size of gI2, 932 
St Choice of . 1113 ‘* Dimensions of, used in esti- 
¥: Coal-tar “ 1154, 1167 mates . : , : . 1057 
3 Cobblestone L141 ‘“* Graphical determination of 
‘ Construction of . 1141 bending moment on 936, 939 
Me Cost of A 1118, 1128 ‘* grip of, Determining the 1018 
7 Different kinds of 1112 “ “hip, Design of. 936 
ts Distillate. 1168 “ Length of 1024, 1037 
fs Durability of 1116 ‘“ Maximum bending moment 
sf Economy of 1117 5 ae , f " 913 
= Essential qualities ‘* Minimum diameter of 899, 1020 
of Fs " TER LITS “ Position of , , 886 
Bs Granite-block 1143 ‘** Position of bearing on 925 
as Life of . 1116 “Resisting moments of, how 
a Macadam 1146 determined . 4 : Se ites 
“6 Maintenance of . 1120 ‘* Screw ends of . g 1019 
= Materials used for . 1129 “« Shearing stress allowed on 807 
- Objectiof ‘ ee ey ‘* Table of resisting moments 
ud Rock-asphalt . « 1163 rae ae . : ° ° sg8s 


PAGE 

Pitch, Final or resultant, how de- 
termined . : = OTE 
‘“* of rivetsin batten plates . 946 
“of rivets in beam flanges 967, 971 
“ of rivets in cover-plates LOA: 
“ of rivets in portal bracing . 959 

“ of rivets, Limiting ‘values 


Okwe . : : 898, 964 

‘Ss (Minerals? . . A « | t1g6 

Plate beam hangers A : . 1067 

“ .sirders.. A - : oan 009 
‘© girders, Allowed _ shearing 

stress in web of . ; 859, 877 


“© girders, Assumed distribu- 
tion of tension and com- 
pression in . ° «4. 850 

“ girders, Effective dentn OL SO 

‘* girders, Minimum thickness 


of webof . . 5 elie 
‘* girders, Position of figndes 

on web ; 4 +P tslstss 
‘“ girders, Stiffening of d 7, S59 


girders, Thacher’s specifica- 
tions relating to . : S75 

Plates, Design of . ; - 2) O45 
i Maximum widthof . Fae ete 
ie Reenforcing, at pinholes . goo 

Portal bracing, Designof . at okt 
vo Designof . A . 842 


3 Functions of a. é Ae pas 
4 Stresses in braced 4 e7OS 
“$ Stresses in latticed’ . eo 
< Weight of, used in esti- 
mates 3 . ; LOSS 
Possession, Adverse : : - 1098 
Position of loads for maximum 
bending moment . - 802 


ee of pins . ; : . 886 
Posts, end, Design of : 833, 941 
‘* intermediate, Design of Aye, Gh: 
Pratt truss, Condition of loading, 
for maximum stress . . FOO 
truss, Description of . . 689 
“Sotruss, Hormulas fon chord 
stressesin . : se 
truss, Graphical determi. 
tion of stresses in 3 694, 707 
truss with curved orinclined 


te 


se 


“6 


chords . $ 5 773 
Preparing iron for painting . . 081 
Proportioning material for ten- 
sion members 5 ; : Or? 
R PAGE 

Radius of gyration, Approximate 
formulas for value of . ; ao Beh 


INDEX 


PAGE 
Radius of gyration, Cases in which 
formulas give least . R27, 
‘of gyration in usual com- 
pression members . : oer 
Railing for bridges . F 1072 
Railroads, Location of, éotapared 
with location of highways . 5 efets! 


Railways, Asphalt paving of . 1162 
Ramming of brick pavements 


ee 


1170 
of stone pavements trad 
of wood pavements 5 Line 
Rankine’s formula forcolumns . 823 
Reaction in truss, Determining . 6096 
Reactions for wind pressure at 


ec 


foot of end posts Seip’ 
Recessed nut . 5 . . ro2L 
Records of tiehtey: s - : + x0x6 
= of street grades - 1087 
Red-lead paint . F : ; . 1076 
“lead paint, Proportions for 
mixing . 3 ; ; - 1080 
7, lead, Use ota, : ; . 1079 
Reenforcing plates at pinholes . goo 
Relocation of roads . ‘ ° + « LORS 
Repairs of roads 4 - : ron 7 
Repose, Angleof . - . 1008, 1106 


Resistance, Grade, in highways 999, 1008 


- grade to traction. 1104 

ee of paving material to 
crushing . A 7 drge 
ds totraction . 5 + ¥ 110% 
Resisting length of roads : - 1008 
ae moment of pins 2 A Nok 
Resultant pitch of rivets A =) OFT 
Right of way . 4 2 1017 


Rivet holes, Considers’ in de- 
termining net section se OLS 
holes, Distance from, to 
back of angle . . = OSS 
holes, Distance from, to 
back of channel . tet OAE 
holes, Distance from, to 
edge of piece , - 898, go2 
Riveted girders ; A A - 689 


oe 


ee 


és 


oo trusses E ‘ ° - 689 
Rivets, Arrangement of, in batten 
plates ‘ c +) 946 
it Arrangement ae: in cover- 
plates < . + 104m 


e Arrangement He in pin 


plates 5 i 5 © 924 
bearing on, Determining . 920 
Bearing stress allowed 

on ; - 807, 921 
Countersunk A : 1083 
Dimensions of . : 1038 


INDEX XX1 

PAGE PAGE 

Rivets, Ordering . : <ro48 Section modulus. ; : 7a TOO3 
re Limiting valine: of pitch Shear at any point of uniformly 

of : ~ : : 898, 964 loaded beam 731, 968 


“ Machine and field driven . 808 
number of, Determin- 

ing ‘ 919, 935, 953, 986 
- iearine on, Determining g18 
os Shearing stresses, allowed 


on . = 897, 921 

‘Specifications relating to .  go2 

es Usual sizesof . : . 898 
“., Weight of, Used in esti- 

mates . 1058 

Road machines : : 1036 

-* + metal = . . . 1025 

Roadbed . : 3 1032 


Roads, Alinement of é : > 909 


ce Broken-stone » 1025, 1033, 1038 


he Comparison of , . 1006, 1009 
es Construction of . , werogt 
aE Drainage of F 4 . I01Ig 
sbi Earth . . . 1030, 1035, 1038 
‘s Gravel . F . 1028, 1034 
‘* Location of . : « Q07.-rorT 
= Maintenance of . é 1037 
a Materials for ‘ : » To2s5 
Me Objections to steep . - 999 
v Qualities of good » 995, 1006 - 
oe Relocation of * ‘ ErOTS 

Roadway, Construction of . 1033 
ie Cross-section of (high- 
ways) . - ' - 1018 
bs Cross-section of, for 
streets . 1056 
+ Width of, for nts orave 1018 
ie Width of, for streets 1055 
Rock asphalt. & ‘ : ee ei 
‘* asphalt pavements 1163 


Rods, Sway ‘ ‘ R - - | 795 


Rollers, Expansion . : + QO, 1005 
Rolling friction ; ITOI 
Ropes, Strength of, aud Diets 
sions of . , F Ob 
Ruling grade of hipiways 1005 
Rust, Protection of bridges from . 1075 
Ss PAGE 
Safety of apavement . : IlI4 
Sand . s ‘ : : i 2 <I139 


‘“* for cement, Quality of . “973 


Sandstone . ; 4 ‘ ‘ III3 
Mg block pavement 1145 
Screw ends of pins, Dimensions of 1020 


‘ends, Specifications relating 
TOn ; 5 : - . 899 
** ends upset, Dimensions of 989 


at point of maximum bend- 


ing : 2 . - AV es 
“« diagram, Stresses deter- 
mined by . ‘ 733 


“Effect of negative end. lozd 710 
from live and dead load, 


Finding the 7 : . 710 
‘“ ~Maximum,infloorbeam . = 731 
‘** Single and double / 2 903 
“Stresses dueto . : fo 735 
‘“* Value of, for maximum 


stresses in web members 
and vertical posts. . . FOR 
Shearing stress allowed on pins . 897 


2 stress allowed on 
rivets. 897, 921 

Hy stress allowed on web of 
girder . 859, 877 

bs stress on rivets, Deter- 
mining the . ; . 918 
Shipping bill, Making a . 1048 
Shoe plates . , : : . 1005 
‘* plates, Bending moment on_ 100g 


plates, Formula for thickness 
ory. ; : ; ‘ +, Torr 


plates, Proportioning of 1005 
‘* strut, Design of . 848, 965 
Shop drawings, Date given in 1027 
‘* lists, Making - 1027 
Sidewalk brackets . : : - 798 
Sidewalks (see also Footways) 1067 
* Supporting . ; e705 
Simple truss. “ : : . 686 
Single beam hanger - 1066 
“quadrangular, single- inter- 
section truss - “ 5 689 
Slope, Lateral, of streets. ; 1078 
Soft steel, Properties of, required 
by specifications . ; 810 
** steel, Weight and dpecifia 
gravity of rolled shapes of. 878 
Sole plate . : “ - » 1005 
Spacing of lattice pare : - s 946 
Span of atruss. : : : - 686 
Specifications . ‘ ; 2 eo 81s 
be for highway 
bridges, Cooper’s 869 
e Lewis’s . : 877 
My relating to anchor 
bolts rs gor 
os relating to details bas: go2 
a relating to floor . 861 


relating torivets . goz 


XXil INDEX 
PAGE PAGE 
Specifications, Thacher’s : 875 Stresses, Determination of, by 
Spikes, Weight and dimensions stress and shear dia- 
tre : : O51 grams. . : 733 
Splices, Use ge in foints 898, 950 se due to ben anes mo- 
Standards of shoe : 1005 ments . . : ae 
Static load on bridge ; : . 690 Ss duetoshear . : a 2735 
Statutes of limitation 1098 Ms Floorbeam . ~ 9a6 
Steel, Advantages of, over sy from varying eels - 692 
wroughtiron . j 808 = in braced portals .. « § 795 
he Coefficient of elasticity of 811 . in chords, Graphical de- 
a Coefficient of expansion of 1007 termination of . ; ~ G07; 
hs Cooper’s specifications re- a in curved chords 4515 753 
lating to . : ; . 869 cs in Howe truss ‘ ad Sp 7AZ 
ie Different gradesof . . 810 sf in Petit truss 787, 789 
se Elastic limit of . 811 in Pratt truss . 694, 707 
se Grades of, used in Uaiee oe in truss determined 
work . : . * ve oro graphically , ; 696 
"y Growing useof . : 5 ve kish, S in truss with ‘welined 
+f Structural . ; j . 807 chords 765, 768 
ro = Wists htror = *. j 25 2o70 rf in Warren girder . = agai 
Stiff suspenders, Copibreaates in. 8977 es in web members . Fe {0-05 
Stiffened chords : ‘ P peso a in Whipple truss . a 775 
“f chords, Compression Stringers, Maximum bending mo- 
allowed on . ; Ory ment in 5 : . 802 
Stiffeners in floorbeaiis . ; . 972 a Metal ; : : 1062 
re in plate girders ; 859, 876 Structural steel 3 < - 807 
Stirrup : , : : : - 908 Strut resistance of pin pintads - 956 
Stock list - ; 1034 Struts . ; 3 ‘ 5 - 686 
Ps Matedial cavsiwa in ; . I04I Subgrade . ‘ ; 5 A . 1032, 
Stones, Crossing : 1182 Subpanel . . ° . : i ar 
Straight-line formula. : - ~ 829 Sitbstrat ; ° : : » 795 
Strain sheet ; ‘ - oy, £733 Subtie : 786 
Streets (see also Rosdwank, Surveying for the location of Aish 
pe and avenues 1045 ways ; F : ; . 1000 
ve Arrangement of 1046 Sway rods ? : 5 . = 705 
A Crown of 1057 Swedged bolt : 1017 
‘* Curved 5 : . - 10o5t1 Symmetricaltruss . P : - 685 
os Intersections of . 1071 
- line of, Locating and per- 
petuating ae 3 - 1089 T PAGE 
os Location of togo ©0-- Telford roads ‘ 1025 
7 Width of . P . rosa - Temperature; Varevions of, pro- 
Strength of I beams ; ; - 1064 vided for in bridge work QOI, 1007 
oa Ultimate, for steel . . 8x0 ‘Tensile stresses, Formulas for, ; 
ic Ultimate for wrought founded on fatigue of metals . 873 
iron , : . 809 Tension members oftruss . . 686 
Stress line of action in eee mem- x members, -Proportioning 
bers . 687 of 7S : ; : . | Siz 
<  -shestt. « ; ) °932 Be members, subject to com- 
** sheet, Complete oe m of . 866 pression . 687, 858 
Stresses allowed on floor joists . 863 ee members, Unit stresses 
a Bending, due to weight of allowed for . : 43. 8rd! 


member . ; : . 880 
= Counter : : - 709 
re Determination ate by sec- 

tions and moments - 5 700 


members, Usualforms of 816 
web members, Design of 986 
Tests for abrasion ; 1130 
Thacher’s specifications . A - 9875 


INDEX 


PAGE 

Theoretical length of Kaa mem- 
bers 7 . : 825 

Thickness, ircivined in Re rid ee e 
members : < m - « 825 
Through bridges. . . o 6687 
Ties. 3 r ; ‘ - . 686 
‘- Design of . A : : 986 

Timber, Unit stress allowed on, 
for bending . 863, 876 

a Unit stress allowed on, 
forcompression . . 876 

ir Unit stress allowed on, 
for shearing . : 876 

a Usual sizes of, carried in 
stock : 1044 

or Varieties of, use - for 
joists * - a 804 
Tonnage of traffic over paveniente 1124 


Toughness of paving materials . 1131 
Traction, Resistance to, in high- 


ways - é ee TION 
Tractive force hee Practiam 
i power of horses . 1108 
Traffic, Tonnage of (see arahagel 
Trap rock . ; A 2 - ye xIaA 
Treatment, Chemical, of paving 
blocks. © . : : - eS Ce 
Truss . : F ; 3 » 685 
‘* Baltimore ; . - By hh 
<-Camel-back . - : 7. 973 
“> Cantilever . ‘ : . 686 
se Gomtinuous, ~~ : ° - 686 
‘“ Essentialelement of . 3. 685 
** External forces of - = = 0on 
‘“* Howe : : . : ee Tae 
‘““~Membersof . : : . 686 
Se retit - : 5 706 
>) -Praté, single- quadeaneitar, 
single-intersection . - 689 
“« Simple . : ‘ : - 686 
a opan ot. : P : - 686 
‘** Svmmetrical . : : Se OsS 
‘© Whipple. , : : 73 


‘* withinclined chords . * 749 
Turnbuckles, Dimensions of . OR 


oe Position of, on coun- 
ters : . . go2 
U PAGE 


Uniform load . ‘ ° - 690 
Unit stresses allowed for tension 
members . ‘ A Fad Poh’ 
‘* stresses allowed on medium 
steel . ; ‘ : A tke) 


“stresses allowed on timber . 876 


XXill 
PAGE 
Unsymmetrical sections . . - 1084 
Upper lateral system, Graphical 
determination of stresses in s) SAU; 
Upset ends, Dimensions of . - 989 
“* ends, Length of bars hav- 
ing : : 4 , 1037 
“sends, Specifications rela- 
ting to : : . = Og 
vi PAGE 
Varying load, Stresses from . - 602 
WwW PAGE 
Warren girder. “ = 6744 
ae girder, Grapiical es 0 
mination of stressesin . 745 
Washers for boltsin wheel guards 1049 
‘ for pins 1025 
Washington, City of, Pennine the 1048 
Web members, Design of : Fa telshe. 
‘* “members, Economical incli- 
nation of A ; : 749 
‘“* members, Maximum eereaain 
LNs : ; ° » 700 
“plates, Maximum shearing 
stress in ; . : 859 
‘* stresses, Error in the eters 
mination of maximum - 793 
‘* stresses, Short method for 
determining ‘ : 737 
Wedge bolt = ‘ : 1017 


Weight, Maximum and minimum, 
of wrought-iron chan- 
nelsandangles . 830 

of floorbeam 727, 1058 

2 of materials used in esti- 


mates : : 3 - 1058 
ie of members, Estimating 

the . ; ‘ : » 1055 

ok of nails and spikes 1051 
aS of rolled sections of 
wrought iron, high, and 

soft steel : ; . 878 

e. of steel : P . 878 

Me of timber bridge por «5706 

4 of wrought iron : 828, 878 

Wheel guards, Details of ‘ - 1049 

e loads ; : = A - 690 

me loads, Concentrated , 5.) SOx 
Whippletruss, Assumption regard- 
ing distribution of 

stresses in i - 975 

y truss, Description of » 973 


ia 


truss, Graphical deter- 
mination of stresses in 775 
White-lead paint. ‘ . - 1076 


XXIV 

PAGE 

Width, Maximum, of plates in com- 
pression . : ; » 825 
‘of flange of channel . A tiete! 
+ Soft truss Gwe > < mOrS 
Wind load, Assumed amount of . 690 
‘* load, Stating the . . « 691 

‘* pressure, Transmitting to 


and by the portal F a7 tS 
‘¢ pressure, Provision for, in 

chords and end posts 815, 850 
‘* pressure, Provision for, in 


designing pins . 3 - 929 
‘* pressure, Reactions from, at 
feet of end posts ; - 720 


** stresses, Graphical deter- 
mination of, in lower lat- 


eral system : 5 711, 714 
“* stresses, Graphical deter- 
mination of, in upper lat- 
eral system : : 717 
“ stresses, Transmitted to the 
anchorage . 5 ° . 715 
Weoehler’s law relating to fatigue 
of metals “ ; - - 872 


INDEX 


PAGE 

Wood pavements . ° ° . 2147 
Pe) paving se. ‘ . ° . 1138 
Wooden hub guards ; 4 + 1071 


Working drawings . ; : - 896 
Mh BELESSESa as . . ot eres 
oh stresses allowed on me- 


dium steel members 869, 874 
* stresses allowed on 
wrought-iron compres- 


sion members 824, 874 
os stresses allowed on 
wrought-iron tension 
members 5 : 814, 874 
Wrought iron, Coefficient of ex- 
pansion of . ‘ . 1607 
id iron, Properties of, re- 


quired by specifications 809 


es 


iron, Supposed advan- 
tages of, over steel . 808 

os iron, Use of, in bridge 
work : : : a Oy 
“ iron, Weight of A . 828 


< iron, Weight of rolled 
sections of . ° - 830 





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